bluuebunny/crossref_metadata_2025 huggingface dataset:
Mitochondrial DNA Variation in the Ozark Highland Members of the Banded Sculpin Cottus carolinae Complex
Authors: Kinziger Andrew P. , Goodman Damon H. , Studebaker Rebecca S.
Published: December 2007

The goal of this study was to determine whether variation in mitochondrial DNA (mtDNA) sequence data is concordant with morphological divergence in the five Ozark Highlands members of the complex of banded sculpin Cottus carolinae: Eyelash sculpin, fringehead sculpin, Black River race, grotto sculpin, and midlands race. We generated a phylogenetic hypothesis for the banded sculpin complex based on a data set composed of 841 base pairs of mtDNA (ATPase‐8 and ATPase‐6) for 58 individuals representing all banded sculpin complex members that occur in the Ozark Highlands and comparative material collected outside of the highlands. Divergence in mtDNA was found to be generally concordant with morphological distinctiveness in the fringehead sculpin, eyelash sculpin, Black River race, and grotto sculpin; however, genetic divergence of these taxa was generally low (sequence divergence maximum = 0.2‐1.4%) relative to the marked morphological distinctness exhibited by these taxa. In contrast, the midlands race was recovered as nonmonophyletic and contained a relatively large amount of within‐race sequence divergence (uncorrected p‐distance = 0‐5%), illustrating that this race is poorly understood.
Characteristics of urban run-off derived sediments captured by proprietary flow-through stormwater interceptors
Authors: Faram M.G. , Iwugo K.O. , Andoh R.Y.G.
Published: December 2007

Sediment entrained in urban run-off is acknowledged as being an important carrier of pollutants. The paper reports on the physical and chemical characteristics of sediments captured by six installations of a proprietary interceptor device. The sites, located in the United Kingdom and the Republic of Ireland, were selected to represent a range of urban contexts. Particle D50 values were found to range from 7 to 112 μm, corresponding with ranges reported for stormwater ponds. Heavy metal and hydrocarbon concentrations were also found to vary, with the highest corresponding to the most established and heavily trafficked sites. Further to confirming the ability of the interceptor to remove contaminated sediments, useful insights are provided into the interrelation between sediment characteristics and site conditions.
Contributing to the sustainable use of stormwater: the role of pervious pavements
Authors: Jayasuriya L.N.N. , Kadurupokune N. , Othman M. , Jesse K.
Published: December 2007

The city of Melbourne, Australia is experiencing a water crisis with potable water storage reservoirs at an all time low. With increasing urbanisation there is an ever increasing need to research and explore sustainable water management initiatives. There is potential to minimise the negative impacts of stormwater runoff and augment dwindling supplies of potable water through adoption of pervious paving technology. The traditional approach to stormwater management has focused on constructing drainage networks to carry stormwater away from developed areas as quickly as possible to avoid the risk of flooding. The main aim of this research project was to establish relationships between rainfall intensity, infiltration rate and pervious pavement runoff and to examine the improvement to stormwater quality after infiltrating through pervious pavements. This paper describes the laboratory experiment set-up to determine the infiltration patterns and stormwater quality improvement for simulated storms precipitating on pervious pavements. Next, the scaling-up of the experimental rig to a field-based trial is explained. Preliminary results from this work are presented to demonstrate the potential benefits of pervious pavements in the Australian landscape.
An investigation of wash-off controlling parameters at urban and commercial monitoring sites
Authors: Berretta C. , Gnecco I. , Lanza L.G. , La Barbera P.
Published: December 2007

The relationship between the parameters of the wash-off function and the controlling hydrologic variables are investigated in this paper, assuming that the pollutant generation process basically depends on the watershed rainfall-runoff response characteristics. Data collected during an intense monitoring program carried out by the Department of Environmental Engineering of the University of Genova (Italy) within a residential area, an auto dismantler facility, a tourism terminal and a urban waste truck depot are used to this aim. The observed runoff events are classified into different TSS mass delivery processes and the occurrence of the first flush phenomenon is also investigated. The correlation between the mathematical parameters describing the exponential process and the hydrological parameters of the corresponding rainfall-runoff event is analysed: runoff parameters and in particular the maximum flow discharge over the time of concentration of the drainage network are proposed as the controlling factor for the total mass of pollutant that is made available for wash-off during each runoff event
CSO treatment strategy based on constituent index relationships in a highly urbanised catchment
Authors: Piro P. , Carbone M. , Garofalo G. , Sansalone J.
Published: December 2007

In urbanising catchments the variability of particulate matter (solids) and oxygen demanding constituents of wet weather and dry weather characteristics result in variable treatment effectiveness from physical unit operations and biological unit processes. Higher organic concentrations during dry weather flow are more amenable to biological unit processes while the higher inorganic loads generated largely by urban wet weather constituents and much larger flows can be more effectively treated or conditioned by physical unit operations, including ideally preceded by hydrologic controls. This study examines the relationships between total chemical oxygen demand (COD)t, dissolved chemical oxygen demand (COD)d, particulate chemical oxygen demand (COD)p and solids, measured as total suspended solids (TSS). Results also provide an index for selection and optimisation of treatment operations for combined sewer overflow (CSO) loads.
Sewer storage tank performance under climate change
Authors: Butler D. , McEntee B. , Onof C. , Hagger A.
Published: December 2007

This paper describes a study of the potential effects of climate change on the design and performance of sewer storage tanks. A long-term synthetic rainfall time-series has been derived based on the IPPC medium-high emission scenario for a case study in London. Results indicate a 35% increase in the number of storm events that cause filling of the tank and a 57% increase in the average volume of storage required. A method to estimate the required future storage volume for any given return period has been developed and described. Indications are that significantly larger storage volumes will be required to maintain the same level of flood protection.
Temporal evolution and spatial distribution of heavy metals in a stormwater infiltration basin – estimation of the mass of trapped pollutants
Authors: Le Coustumer S. , Moura P. , Barraud S. , Clozel B. , Varnier J.-C.
Published: December 2007

Infiltration systems are widely used to manage stormwater in urban areas but questions about their long term sustainability need to be addressed. The possible pollution of the groundwater and the concentration of pollutant trapped in the soil are of major interest. This article focuses on the concentration of heavy metals found in the top layer of an infiltration basin. Two sampling campaigns have been undertaken 10 months apart and 200 samples were collected and analysed for lead (Pb), zinc (Zn) and copper (Cu). High concentrations were measured at the surface of the system; pollutant build up over time is clearly evident, especially in the lower lying areas, as well as higher concentrations in the oldest part of the system. Finally, the total mass of heavy metals trapped in the top layer of the systems are evaluated.
A metamodel for stormwater detention basins design
Authors: Leviandier T. , Payraudeau S.
Published: December 2007

The aim of storm basins is to protect urban areas against some predefined risk of exceeding a given value of downstream runoff, or a risk of overflow for a bounded storage capacity. This risk results from the combination of a natural hazard and hydraulic properties. The correct way to address this issue is to use a stochastic rainfall model, but it may require unavailable data and be cumbersome to use in the framework of an optimisation procedure. We give the end user a way to by-pass this step, by means of a metamodel. The problem is to calculate the parameters of the probability density function (pdf) of outputs as a function of the pdf of inputs and of the parameters of the dynamic deterministic system between inputs and outputs. We propose to apply a metamodel, which is a new way of designing approximate but generic derived distribution, based on conditional probabilities. For application to dimensioning of basins, the determination of the parameter(s) corresponding to an acceptable risk simply consists of solving an algebraic equation representing the metamodel. The methodology needs usual rainfall statistics and a specific parameter inferred from analysis of storms, or supposed to have a regional value.
Hindered and compression settling: parameter measurement and modelling
Authors: Stricker A.-E. , Takács I. , Marquot A.
Published: December 2007

The Vesilind settling velocity function forms the basis of flux theory used both in state point analysis (for design and capacity rating) and one-dimensional dynamic models (for dynamic process modelling). This paper proposes new methods to address known shortcomings of these methods, based on an extensive set of batch settling tests conducted at different scales. The experimental method to determine the Vesilind parameters from a series of bench scale settling tests is reviewed. It is confirmed that settling cylinders must be slowly stirred in order to represent settling performance of full scale plants for the whole range of solids concentrations. Two new methods to extract the Vesilind parameters from settling test series are proposed and tested against the traditional manual method. Finally, the same data set is used to propose an extension to one-dimensional (1-D) dynamic settler models to account for compression settling. Using the modified empirical function, the model is able to describe the batch settling interface independently of the number of layers.
Occurrence of 70 pharmaceutical and personal care products in Tone River basin in Japan
Authors: Nakada N. , Komori K. , Suzuki Y. , Konishi C. , Houwa I. , Tanaka H.
Published: December 2007

The occurrence of 70 pharmaceutical and personal care products (PPCPs) was investigated in the Tone River. The river has the largest basin in Japan, and the water is utilized not only for farming, but also as a source of water supply. One day in both January and October 2006, surface waters in the river and its tributaries and effluents from sewage treatment plants (STPs) directly discharging into the Tone River were collected, the location of which ranged over 150 km along the river. The 70 PPCPs in the samples were concentrated by solid phase cartridge and were measured by LC-MS/MS using three analytical methods. Fifty-seven PPCPs were detected in one or more samples. Bezafibrate, caffeine, carbamazepine, clarithromycin, crotamiton and sulpiride were frequently detected. Mass flow profiles of some PPCPs (e.g., crotamiton) were comparable to cumulative inhabitants in the basin, suggesting that these PPCPs could be markers of population. Total load of each PPCP into the basin from upstream, the tributaries, and the STPs were calculated. The contribution of selected PPCPs from the tributaries with lower sewerage system coverage was dominant compared to those from upstream and the STPs, suggesting the installation of sewerage systems is necessary to reduce the load of PPCPs in the Tone River basin.
N-nitrosodimethylamine formation during treatment with strong oxidants of dimethylamine containing water
Authors: Andrzejewski P. , Nawrocki J.
Published: December 2007

The aim of the paper is the evaluation of the possibility of NDMA formation, as a result of strong oxidants reacting with DMA. Summarized results of investigations on N-nitrosodimethylamine formation as a result of dimethylamine reactions with chlorine dioxide, ozone and hydrogen peroxide are presented. Preliminary results of experiments on NDMA formation as a result of DMA reactions with permanganate are also shown.

The experiments on dimethylamine reactions with chlorine dioxide, hydrogen peroxide and permanganate were carried out at room temperature under static conditions. Ozonation experiments were carried out at room temperature in a semi-continuous mode. Water samples from all experiments described above were collected during the experiment itself and subsequently analyzed with HPLC-IE with UV-Vis detector at 230 nm. NDMA formation was also confirmed by GC-LRMS.

NDMA forms as a result of chlorine dioxide, ozone, hydrogen peroxide or permanganate reactions with dimethylamine. both in the presence as well as in the absence of ammonia ions. The presence of nitrites and nitrates in a post-reaction mixture suggests that NDMA are formed as the result of DMA reactions with nitrites. Thus the mechanism of NDMA formation with these oxidants is different than that described by Mitch et al. and Choi et al.

The results also showed a conversion ratio of DMA to NDMA of even up to a single percent (with relation to amines), a simultaneous decrease of NDMA formation potential with a decrease of pH, however, in the case of chlorine dioxide application, a maximum conversion ratio was observed, as well the NDMA formation potential is strongly dependent on the oxidant/DMA ratio.
Biocides used in building materials and their leaching behavior to sewer systems
Authors: Burkhardt M. , Kupper T. , Hean S. , Haag R. , Schmid P. , Kohler M. , Boller M.
Published: December 2007

There is increasing concern about diffuse pollution of aquatic systems by biocides used in urban areas. We investigated sources and pathways of biocides significant for the pollution of storm water runoff. Main sources seem to be building envelopes, i.e. facades (paints, plasters) and roof sealing membranes. First results from a defined urban catchment drained by a separated sewer system without any agricultural activities reveal a substantial occurrence. Even after the first flush, concentrations of terbutryn, carbendazim, mecoprop as well as Irgarol 1051® and its metabolite exceeded the Swiss water quality standard of 0.1 μg/L. In laboratory experiments, leaching of mecoprop used as a root protection agent in bitumen sheets for roof waterproofing was determined. The concentrations differed in 16 different sheets two orders of magnitude, depending on the product composition. Using optimized products, it is expected to be the most efficient and sustainable way to reduce the environmental impact. To understand transport dynamics and environmental risk, further storm water events will be analyzed. Based on the ongoing project URBIC, first measures will be proposed to limit the release to surface and ground water.
Elimination of micropollutants and hazardous substances at the source in the chemical and pharmaceutical industry
Authors: Blöcher C.
Published: December 2007

Industrial wastewater, especially from chemical and pharmaceutical production, often contains substances that need to be eliminated before being discharged into a biological treatment plant and following water bodies. This can be done within the production itself, in selected waste water streams or in a central treatment plant. Each of these approaches has certain advantages and disadvantages. Furthermore, a variety of wastewater treatment processes exist that can be applied at each stage, making it a challenging task to choose the best one in economic and ecological terms. In this work a general approach for that and examples from practice are discussed.
Estrogenic personal care products in a greywater reuse system
Authors: Andersen H.R. , Lundsbye M. , Wedel H.V. , Eriksson E. , Ledin A.
Published: December 2007

The occurrence and fate of parabens in a greywater system was assessed. The potential for removal of residual paraben concentrations in effluent greywater with chlorine dioxide was also investigated. The influent to the greywater plant was characterised by considerable variation, with concentrations from below the detection limit to 40 μg/L and the five commonly used parabens in consumer products were frequently detected. After the biological treatment only two paraben were detected with concentration from 65–120 ng/L. Chlorine dioxide treatment of the biologically treated effluent with dosages down to 0.75 mg/L resulted in more than 97% reduction of all parabens. Formation of the by-product chloroform was insignificant from the chlorine dioxide treatment.
Monitoring, removal and risk assessment of cytostatic drugs in hospital wastewater
Authors: Lenz K. , Mahnik S.N. , Weissenbacher N. , Mader R.M. , Krenn P. , Hann S. , Koellensperger G. , Uhl M. , Knasmüller S. , Ferk F. , Bursch W. , Fuerhacker M.
Published: December 2007

Cytostatic agents are applied in cancer therapy and subsequently excreted into hospital wastewater. As these substances are known to be carcinogenic, mutagenic and toxic for reproduction, they should be removed from wastewater at their source of origin.

In this study the fate and effects of the cancerostatic platinum compounds (CPC) cisplatin, carboplatin, oxaliplatin, 5-fluorouracil (5-FU) and the anthracyclines doxorubicin, daunorubicin and epirubicin were investigated in hospital wastewater. Wastewater from the in-patient treatment ward of a hospital in Vienna was collected and monitored for the occurrence of the selected drugs. A calculation model was established to spot the correlation between administered dosage and measured concentrations. To investigate the fate of the selected substances during wastewater treatment, the oncologic wastewater was treated in a pilot membrane bioreactor system (MBR) and in downstream advanced wastewater treatment processes (adsorption to activated carbon and UV-treatment). Genotoxic effects of the oncologic wastewater were assessed before and after wastewater treatment followed by a risk assessment.

Monitoring concentrations of the selected cytostatics in the oncologic wastewater were in line with calculated concentrations. Due to different mechanisms (adsorption, biodegradation) in the MBR-system 5 - FU and the anthracyclines were removed < LOD, whereas CPC were removed by 60%. In parallel, genotoxic effects could be reduced significantly by the MBR-system. The risk for humans, the aquatic and terrestrial environment by hospital wastewater containing cytostatic drugs was classified as small in a preliminary risk assessment.
Algebraic Logic, Where Does it Stand Today?
Authors: Ahmed Tarek Sayed
Published: December 2007

This is a survey article on algebraic logic. It gives a historical background leading up to a modern perspective. Central problems in algebraic logic (like the representation problem) are discussed in connection to other branches of logic, like modal logic, proof theory, model-theoretic forcing, finite combinatorics, and Gödel's incompleteness results. We focus on cylindric algebras. Relation algebras and polyadic algebras are mostly covered only insofar as they relate to cylindric algebras, and even there we have not told the whole story. We relate the algebraic notion of neat embeddings (a notion special to cylindric algebras) to the metalogical ones of provability, interpolation and omitting types in variants of first logic. Another novelty that occurs here is relating the algebraic notion of atom-canonicity for a class of boolean algebras with operators to the metalogical one of omitting types for the corresponding logic. A hitherto unpublished application of algebraic logic to omitting types of first order logic is given. Proofs are included when they serve to illustrate certain concepts. Several open problems are posed. We have tried as much as possible to avoid exploring territory already explored in the survey articles of Monk [93] and Németi [97] in the subject.
Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle
Authors: Steprāns Juris
Published: December 2007

It is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.
What is Tarski'sCommonConcept of Consequence?
Authors: Jané Ignacio
Published: December 2007

In 1936 Tarski sketched a rigorous definition of the concept of logical consequence which, he claimed, agreed quite well with common usage—or, as he also said, with thecommonconcept of consequence. Commentators of Tarski's paper have usually been elusive as to what this common concept is. However, being clear on this issue is important to decide whether Tarski's definition failed (as Etchemendy has contended) or succeeded (as most commentators maintain). I argue that the common concept of consequence that Tarski tried to characterize is not some general, all-purpose notion of consequence, but a rather precise one, namely the concept of consequence at play in axiomatics. I identify this concept and show that Tarski's definition is fully adequate to it.
What is Neologicism?
Authors: Linsky Bernard , Zalta Edward N.
Published: December 2007

Logicism is a thesis about the foundations of mathematics, roughly, that mathematics is derivable from logic alone. It is now widely accepted that the thesis is false and that the logicist program of the early 20th century was unsuccessful. Frege's [1893/1903] system was inconsistent and the Whitehead and Russell [1910–1913] system was not thought to be logic, given its axioms of infinity, reducibility, and choice. Moreover, both forms of logicism are in some sense non-starters, since each asserts the existence of objects (courses of values, propositional functions, etc.), something which many philosophers think logic is not supposed to do. Indeed, the tension in the idea underlying logicism, that the axioms and theorems of mathematics can be derived as theorems of logic, is obvious: on the one hand, there are numerous existence claims among the theorems of mathematics, while on the other, it is thought to be impossible to prove the existence of anything from logic alone. According to one well-received view, logicism was replaced by a very different account of the foundations of mathematics, in which mathematics was seen as the study of axioms and their consequences in models consisting of the sets described by Zermelo-Fraenkel set theory (ZF). Mathematics, on this view, is just applied set theory.
Classification from a Computable Viewpoint
Authors: Calvert Wesley , Knight Julia F.
Published: December 2007

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence, in terms of relatively simple invariants. Where this is impossible, it is useful to have concrete results saying so. In model theory and descriptive set theory, there is a large body of work showing that certain classes of mathematical structures admit classification while others do not. In the present paper, we describe some recent work on classification in computable structure theory.

Section 1 gives some background from model theory and descriptive set theory. From model theory, we give sample structure and non-structure theorems for classes that include structures of arbitrary cardinality. We also describe the notion of Scott rank, which is useful in the more restricted setting of countable structures. From descriptive set theory, we describe the basic Polish space of structures for a fixed countable language with fixed countable universe. We give sample structure and non-structure theorems based on the complexity of the isomorphism relation, and on Borel embeddings.

Section 2 gives some background on computable structures. We describe three approaches to classification for these structures. The approaches are all equivalent. However, one approach, which involves calculating the complexity of the isomorphism relation, has turned out to be more productive than the others. Section 3 describes results on the isomorphism relation for a number of mathematically interesting classes—various kinds of groups and fields. In Section 4, we consider a setting similar to that in descriptive set theory. We describe an effective analogue of Borel embedding which allows us to make distinctions even among classes of finite structures. Section 5 gives results on computable structures of high Scott rank. Some of these results make use of computable embeddings. Finally, in Section 6, we mention some open problems and possible directions for future work.
Schemata: The Concept of Schema in the History of Logic
Authors: Corcoran John
Published: December 2007

Schemata have played important roles in logic since Aristotle'sPrior Analytics. The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski's 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano's second-order Induction Axiom is approximated by Herbrand's Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo's second-order Separation Axiom is approximated by Fraenkel's first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is atemplate-textorscheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with aside conditionthe template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, calledinstancesof the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata.
Closing the Circle: An Analysis of Emil Post's Early Work
Authors: de Mol Liesbeth
Published: December 2007

In 1931 Kurt Gödel published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions to mathematical logic and its foundations should not be underestimated. It is the purpose of this article to show that an interest in the early work of Emil Post should be motivated not only by this historical fact, but also by the fact that Post's approach and method differs substantially from those offered by Gödel, Turing and Church. In this paper it will be shown how this method evolved in his early work and how it finally led him to his results.
Degree Structures: Local and Global Investigations
Authors: Shore Richard A.
Published: December 2007

The occasion of a retiring presidential address seems like a time to look back, take stock and perhaps look ahead.

Institutionally, it was an honor to serve as President of the Association and I want to thank my teachers and predecessors for guidance and advice and my fellow officers and our publisher for their work and support. To all of the members who answered my calls to chair or serve on this or that committee, I offer my thanks as well. Your work was both needed and appreciated.

A major component of the efforts of the Association is devoted to our publications. My first important task as President was to deal with the need to reorganize the reviews section of the JSL and eventually to move it to the BSL. Appropriately enough, my first administrative job for the Association, some thirty years ago, was to serve on a committee to plan a reorganization of the reviews. I thank all those who helped with this transition and who took over the task of running the new reviews section. I hope that it will be another thirty years before further major changes are needed in this area and that someone else will be making them.
Randomness and Computability: Open Questions
Authors: Miller Joseph S. , Nies André
Published: December 2007

It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.

Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be hard, we indicate this by the symbol ▶, the criterion being that it is of considerable interest and has been tried by a number of researchers. Some questions are close contenders here; these are marked by ▷. With few exceptions, the questions are precise. They mostly have a yes/no answer. However, there are often more general questions of an intuitive or even philosophical nature behind. We give an outline, indicating the more general questions.

All sets will be sets of natural numbers, unless otherwise stated. These sets are identified with infinite strings over {0, 1}. Other terms used in the literature are sequence and real.
Calibrating Randomness
Authors: Downey Rod , Hirschfeldt Denis R. , Nies André , Terwijn Sebastiaan A.
Published: December 2007

We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness notions going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].

These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set.
Internal Consistency and the Inner Model Hypothesis
Authors: Friedman Sy-David
Published: December 2007

There are two standard ways to establish consistency in set theory. One is to prove consistency using inner models, in the way that Gödel proved the consistency of GCH using the inner model L. The other is to prove consistency using outer models, in the way that Cohen proved the consistency of the negation of CH by enlarging L to a forcing extension L[G].

But we can demand more from the outer model method, and we illustrate this by examining Easton's strengthening of Cohen's result:

Theorem 1 (Easton's Theorem). There is a forcing extensionL[G] of L in which GCH fails at every regular cardinal.

Assume that the universe V of all sets is rich in the sense that it contains inner models with large cardinals. Then what is the relationship between Easton's model L[G] and V? In particular, are these models compatible, in the sense that they are inner models of a common third model? If not, then the failure of GCH at every regular cardinal is consistent only in a weak sense, as it can only hold in universes which are incompatible with the universe of all sets. Ideally, we would like L[G] to not only be compatible with V, but to be an inner model of V.

We say that a statement is internally consistent iff it holds in some inner model, under the assumption that there are innermodels with large cardinals.
Set Theory and C*-Algebras
Authors: Weaver Nik
Published: December 2007

We survey the use of extra-set-theoretic hypotheses, mainly the continuum hypothesis, in the C*-algebra literature. The Calkin algebra emerges as a basic object of interest.
Inner Models and Ultrafilters In L(ℝ)
Authors: Neeman Itay
Published: December 2007

We present a characterization of supercompactness measures for ω1 in L(ℝ), and of countable products of such measures, using inner models. We give two applications of this characterization, the first obtaining the consistency of with ZFC+ADL(ℝ), and the second proving the uniqueness of the supercompactness measure over in L(ℝ) for .
Fragment of Nonstandard Analysis with a Finitary Consistency Proof
Authors: Rössler Michal , Jeřábek Emil
Published: December 2007

We introduce a nonstandard arithmetic NQA− based on the theory developed by R. Chuaqui and P. Suppes in [2] (we will denote it by NQA+), with a weakened external open minimization schema. A finitary consistency proof for NQA− formalizable in PRA is presented. We also show interesting facts about the strength of the theories NQA−and NQA+; NQA−is mutually interpretable with IΔ0 + EXP, and on the other hand, NQA+interprets the theories IΣ1 and WKL0.
On the Equimorphism Types of Linear Orderings
Authors: Montalbán Antonio
Published: December 2007

§1. Introduction. A linear ordering (also known astotal ordering) embedsinto another linear ordering if it is isomorphic to a subset of it. Two linear orderings are said to beequimorphicif they can be embedded in each other. This is an equivalence relation, and we call the equivalence classesequimorphism types. We analyze the structure of equimorphism types of linear orderings, which is partially ordered by the embeddability relation. Our analysis is mainly fromthe viewpoints of Computability Theory and Reverse Mathematics. But we also obtain results, as the definition of equimorphism invariants for linear orderings, which provide a better understanding of the shape of this structure in general.

This study of linear orderings started by analyzing the proof-theoretic strength of a theorem due to Jullien [Jul69]. As is often the case in Reverse Mathematics, to solve this problem it was necessary to develop a deeper understanding of the objects involved. This led to a variety of results on the structure of linear orderings and the embeddability relation on them. These results can be divided into three groups.
Gödel and Set Theory
Authors: Kanamori Akihiro
Published: December 2007

Kurt Gödel (1906–1978) with his work on the constructible universeLestablished the relative consistency of the Axiom of Choice (AC) and the Continuum Hypothesis (CH). More broadly, he ensured the ascendancy of first-order logic as the framework and a matter of method for set theory and secured the cumulative hierarchy view of the universe of sets. Gödel thereby transformed set theory and launched it with structured subject matter and specific methods of proof. In later years Gödel worked on a variety of set theoretic constructions and speculated about how problems might be settled with new axioms. We here chronicle this development from the point of view of the evolution of set theory as a field of mathematics. Much has been written, of course, about Gödel's work in set theory, from textbook expositions to the introductory notes to his collected papers. The present account presents an integrated view of the historical and mathematical development as supported by his recently published lectures and correspondence. Beyond the surface of things we delve deeper into the mathematics. What emerges are the roots and anticipations in work of Russell and Hilbert, and most prominently the sustained motif of truth as formalizable in the “next higher system”. We especially work at bringing out how transforming Gödel's work was for set theory. It is difficult now to see what conceptual and technical distance Gödel had to cover and how dramatic his re-orientation of set theory was.
In the Shadows of the Löwenheim-Skolem Theorem: Early Combinatorial Analyses of Mathematical Proofs
Authors: von Plato Jan
Published: December 2007

The Löwenheim–Skolem theorem was published in Skolem's long paper of 1920, with the first section dedicated to the theorem. The second section of the paper contains a proof-theoretical analysis of derivations in lattice theory. The main result, otherwise believed to have been established in the late 1980s, was a polynomial-time decision algorithm for these derivations. Skolem did not develop any notation for the representation of derivations, which makes the proofs of his results hard to follow. Such a formal notation is given here by which these proofs become transparent. A third section of Skolem's paper gives an analysis for derivations in plane projective geometry. To clear a gap in Skolem's result, a new conservativity property is shown for projective geometry, to the effect that a proper use of the axiom that gives the uniqueness of connecting lines and intersection points requires a conclusion with proper cases (logically, a disjunction in a positive part) to be proved.

The forgotten parts of Skolem's first paper on the Löwenheim–Skolem theorem are the perhaps earliest combinatorial analyses of formal mathematical proofs, and at least the earliest analyses with profound results.
Local Definitions in Degree Structures: The Turing Jump, Hyperdegrees and Beyond
Authors: Shore Richard A.
Published: December 2007

There are Π5 formulas in the language of the Turing degrees, D, with ≤, ⋁ and ⋀, that define the relations x″ ≤ y″, x″ = y″ and so x ∈ L2(y) = {x ≥ y ∣ x″ = y″} in any jump ideal containing 0(ω). There are also Σ6 & Π6 and Π8 formulas that define the relations w = x″ and w = x′, respectively, in any such ideal I. In the language with just ≤ the quantifier complexity of each of these definitions increases by one. On the other hand, no Π2 or Σ2 formula in the language with just ≤ defines L2 or x ∈ L2(y). Our arguments and constructions are purely degree theoretic without any appeals to absoluteness considerations, set theoretic methods or coding of models of arithmetic. As a corollary, we see that every automorphism of I is fixed on every degree above 0″ and every relation on I that is invariant under double jump or joining with 0″ is definable over I if and only if it is definable in second order arithmetic with set quantification ranging over sets whose degrees are in I. Similar direct coding arguments show that every hyperjump ideal I is rigid and biinterpretable with second order arithmetic with set quantification ranging over sets with hyperdegrees in I. Analogous results hold for various coarser degree structures.
Relating First-Order Set Theories and Elementary Toposes
Authors: Awodey Steve , Butz Carsten , Simpson Alex , Streicher Thomas
Published: December 2007

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that the full axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo–Fraenkel set theory (IZF).
The cost of a cycle is a square
Authors: Carbone A.
Published: December 2007

The logical flow graphs of sequent calculus proofs might contain oriented cycles. For the predicate calculus the elimination of cycles might be non-elementary and this was shown in [Car96]. For the propositional calculus, we prove that if a proof of k lines contains n cycles then there exists an acyclic proof with (kn+1) lines. In particular, there is a polynomial time algorithm which eliminates cycles from a proof. These results are motivated by the search for general methods on proving lower bounds on proof size and by the design of more efficient heuristic algorithms for proof search.
Embedding finite lattices into the Σ20 enumeration degrees
Authors: Lempp Steffen , Sorbi Andrea
Published: December 2007

We show that every finite lattice is embeddable into the Σ20 enumeration degrees via a lattice-theoretic embedding which preserves 0 and 1.
An algebraic approach to categories of partial morphisms
Authors: Stefani S. T.
Published: December 2007

In the study of categories whose morphisms display a behaviour similar to that of partial functions, the concept of morphism domain is, obviously, central. In this paper an operation defined on morphisms describes those properties which are related to morphisms being regarded as abstractions of partial functions. This operation allows us to characterise the morphism domains directly, and gives rise to an algebra defined by a simple set of identities. No product-like categorical structures are needed therefore. We also develop the construction of topologies together with the notion of continuous morphism, in order to test the effectiveness of this approach. It is interesting to see how much of the computational character of the morphisms is translated into continuity.
A maximal bounded forcing axiom
Authors: Asperó David
Published: December 2007

After presenting a general setting in which to look at forcing axioms, we give a hierarchy of generalized bounded forcing axioms that correspond level by level, in consistency strength, with the members of a natural hierarchy of large cardinals below a Mahlo. We give a general construction of models of generalized bounded forcing axioms. Then we consider the bounded forcing axiom for a class of partially ordered sets Γ1 such that, letting Γ0 be the class of all stationary-set-preserving partially ordered sets, one can prove the following:

(a) Γ0 ⊆ Γ1,

(b) Γ0 = Γ1 if and only if NSω1 is ℵ1-dense.

(c) If P ∉ Γ1, then BFA({P}) fails.

We call the bounded forcing axiom for Γ1Maximal Bounded Forcing Axiom (MBFA). Finally we prove MBFA consistent relative to the consistency of an inaccessible Σ2-correct cardinal which is a limit of strongly compact cardinals.
Definitions of compactness and the axiom of choice
Authors: Cruz Omar De La , Hall Eric , Howard Paul , Rubin Jean E. , Stanley Adrienne
Published: December 2007

We study the relationships between definitions of compactness in topological spaces and the roll the axiom of choice plays in these relationships.
SN and CR for free-style LKtq: linear decorations and simulation of normalization
Authors: Joinet Jean-Baptiste , Schellinx Harold , De Falco Lorenzo Tortora
Published: December 2007

The present report is a, somewhat lengthy, addendum to [4], where the elimination of cuts from derivations in sequent calculus for classical logic was studied ‘from the point of view of linear logic’. To that purpose a formulation of classical logic was used, that - as in linear logic - distinguishes between multiplicative and additive versions of the binary connectives.

The main novelty here is the observation that this type-distinction is not essential: we can allow classical sequent derivations to use any combination of additive and multiplicative introduction rules for each of the connectives, and still have strong normalization and confluence of tq-reductions.

We give a detailed description of the simulation of tq-reductions by means of reductions of the interpretation of any given classical proof as a proof net of PN2 (the system of second order proof nets for linear logic), in which moreover all connectives can be taken to be of one type, e.g., multiplicative.

We finally observe that dynamically the different logical cuts, as determined by the four possible combinations of introduction rules, are independent: it is not possible to simulate them internally, i.e.. by only one specific combination, and structural rules.
The strict order property and generic automorphisms
Authors: Kikyo Hirotaka , Shelah Saharon
Published: December 2007

If T is a model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.
Minimal groups in separably closed fields
Authors: Bouscaren E. , Delon F.
Published: December 2007

We give a complete description of minimal groups infinitely definable in separably closed fields of finite degree of imperfection. In particular we answer positively the question of the existence of such a group with infinite transcendence degree (i.e., a minimal group with non thin generic).
An axiomatic presentation of the nonstandard methods in mathematics
Authors: Nasso Mauro Di
Published: December 2007

A nonstandard set theory *ZFC is proposed that axiomatizes the nonstandard embedding *. Besides the usual principles of nonstandard analysis, all axioms of ZFC except regularity are assumed. A strong form of saturation is also postulated. *ZFC is a conservative extension of ZFC.
On essentially low, canonically well-generated Boolean algebras
Authors: Bonnet Robert , Rubin Matatyahu
Published: December 2007

Let B be a superatomic Boolean algebra (BA). The rank of B (rk(B)). is defined to be the Cantor Bendixon rank of the Stone space of B. If a ∈ B − {0}, then the rank of a in B (rk(a)). is defined to be the rank of the Boolean algebra . The rank of 0B is defined to be −1. An element a ∈ B − {0} is a generalized atom , if the last nonzero cardinal in the cardinal sequence of B ↾ a is 1. Let a, b ∈ . We denote a ˜ b, if rk(a) = rk(b) = rk(a · b). A subset H ⊆ is a complete set of representatives (CSR) for B, if for every a there is a unique h ∈ H such that h ~ a. Any CSR for B generates B. We say that B is canonically well-generated (CWG), if it has a CSR H such that the sublattice of B generated by H is well-founded. We say that B is well-generated, if it has a well-founded sublattice L such that L generates B.

Theorem 1. Let B be a Boolean algebra with cardinal sequence . If B is CWG, then every subalgebra of B is CWG.

A superatomic Boolean algebra B is essentially low (ESL), if it has a countable ideal I such that rk(B/I) ≤ 1.

Theorem 1 follows from Theorem 2.9. which is the main result of this work. For an ESL BA B we define a set FB of partial functions from a certain countably infinite set to ω (Definition 2.8). Theorem 2.9 says that if B is an ESL Boolean algebra, then the following are equivalent.

(1) Every subalgebra of B is CWG: and

(2) FB is bounded.

Theorem 2. If an ESL Boolean algebra is not CWG, then it has a subalgebra which is not well-generated.