bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the No-Counterexample Interpretation
Authors: Kohlenbach Ulrich 
Published: May 2006

AbstractIn [15], [16] G. Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peano arithmetic. In particular he proved, using a complicated ε-substitution method (due to W. Ackermann), that for every theoremA(Aprenex) of first-order Peano arithmeticPAone can find ordinal recursive functionalsof order type < ε0which realize the Herbrand normal formAHofA.Subsequently more perspicuous proofs of this fact via functional interpretation (combined with normalization) and cut-elimination were found. These proofs however do not carry out the no-counterexample interpretation as alocalproof interpretation and don't respect the modus ponens on the level of the nocounterexample interpretation of formulasAandA → B. Closely related to this phenomenon is the fact that both proofs do not establish the condition (δ) and—at least not constructively—(γ) which are part of the definition of an ‘interpretation of a formal system’ as formulated in [15].
The Complexity of the Collection of Countable Linear Orders of the form I + I
Authors: Beleznay Ferenc 
Published: May 2006

AbstractFirst we prove that the set of countable linear orders of the form I + I form a complete analytic set. As a consequence of this we improve a result of Humke and Laczkovich, who showed in [HL] that the set of functions of the form f º f form a true analytic set in C[0,1]. We show that these functions form a complete analytic set, solving a problem mentioned on p. 215 of [Kl] and on p. 4 of [B]
DOP and FCP in generic structures
Authors: Baldwin John T. , Shelah Saharon 
Published: May 2006

We work throughout in a finite relational language L. This paper is built on [2] and [3]. We repeat some of the basic notions and results from these papers for the convenience of the reader but familiarity with the setup in the first few sections of [3] is needed to read this paper. Spencer and Shelah [6] constructed for each irrational α between 0 and 1 the theory Tα as the almost sure theory of random graphs with edge probability n−α. In [2] we proved that this was the same theory as the theory Tα built by constructing a generic model in [3]. In this paper we explore some of the more subtle model theoretic properties of this theory. We show that Tα has the dimensional order property and does not have the finite cover property.We work in the framework of [3] so probability theory is not needed in this paper. This choice allows us to consider a wider class of theories than just the Tα. The basic facts cited from [3] were due to Hrushovski [4]; a full bibliography is in [3]. For general background in stability theory see [1] or [5].We work at three levels of generality. The first is given by an axiomatic framework in Context 1.10. Section 2 is carried out in this generality. The main family of examples for this context is described in Example 1.3. Sections 3 and 4 depend on a function δ assigning a real number to each finite L-structure as in these examples. Some of the constructions in Section 3 (labeled at the time) use heavily the restriction of the class of examples to graphs. The first author acknowledges useful discussions on this paper with Sergei Starchenko.
Some independence results for control structures in complete numberings
Authors: Jain Sanjay , Nessel Jochen 
Published: May 2006

AbstractAcceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied, among others by Riccardi and Royer, how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Eršov.
On the recursion theorem in iterative operative spaces
Authors: Zashev J. 
Published: May 2006

Abstract.The recursion theorem in abstract partially ordered algebras, such as operative spaces and others, is the most fundamental result of algebraic recursion theory. The primary aim of the present paper is to prove this theorem for iterative operative spaces in full generality. As an intermediate result, a new and rather large class of models of the combinatory logic is obtained.
Topological elementary equivalence of closed semi-algebraic sets in the real plane
Authors: Kuijpers Bart , Paredaens Jan , Van den Bussche Jan 
Published: May 2006

AbstractWe investigate topological properties of subsetsSof the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol forS. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.
The Modernization of International Law
Authors: Wilson George Grafton 
Published: May 2006

Few words have been used with more different meanings than the word “law.” “International law” has likewise had many diverse definitions. The term, international law, is here used to cover the rules and principles which are generally observed in the relations among states. As laws in general become serviceable as their observance becomes regular, so international law becomes serviceable as its rules and principles are generally followed.The modernization of international law would imply the adaptation of international law to modern conditions. Conditions have changed since the old days when “strange air made a man unfree;” when all foreigners were enemies; when emigration was prohibited lest all man-power of a state might leave and there might be no available material for an army; or when such principles generally prevailed as that of Machiavelli, which he enunciates in the following words: “that whoever is the occasion of another's advancement is the cause of his own diminution” (Chap. 3).The development of the family of nations idea, and its extension from the Christian European states to other so-called Christian states, and later to states having a recognized political standing, regardless of religious or ethnic bases, shows the enlarging aspects of international relationship. In order that this relationship might continue, it was necessary that principles generally recognized by those having control of political affairs as worthy of their support should underlie these relationships.
Two Forgotten Studies in Political Psychology
Authors: Lasswell Harold D. 
Published: May 2006

While it is true that every writer on politics has been to some degree an observer of psychological facts, the significance of this has never been so apparent to systematic students as it is today; otherwise, writings of considerable merit in political psychology could scarcely have suffered the fate of the two books referred to in the present study and have disappeared from sight. Dr. J. G. Zimmerman's Essay on National Pride, published at Zürich in 1758, might very well have been the point of departure for extended research into the nature of patriotism and international attitudes; Gottfried Duden's inquiry, Concerning the Essential Differences of States and the Motives of Human Nature, published at Cologne in 1822, stated problems and suggested methods for the examination of the realities of political power which ought to have inspired a century of minute research. Both books fell flat, and it is only in this day of numerous soundings in psychological politics that it has become worthwhile to disinter them.That a book about national pride should have been published two years after the beginning of the Seven Years' War is a sharp reminder that European politics had undergone a transformation. The Reformation was undoubtedly a nationalist movement in many of its phases, but it introduced a series of sectional and party disturbances which intercepted the progress of nationalism. These had subsided, and by the eighteenth century the clash of competing imperialisms became not only a basic fact but a fact of which the men of the age were aware.
Linear reasoning. A new form of the Herbrand-Gentzen theorem
Authors: Craig William 
Published: May 2006

In Herbrand's Theorem [2] or Gentzen's Extended Hauptsatz [1], a certain relationship is asserted to hold between the structures of A and A′, whenever A implies A′ (i.e., A ⊃ A′ is valid) and moreover A is a conjunction and A′ an alternation of first-order formulas in prenex normal form. Unfortunately, the relationship is described in a roundabout way, by relating A and A′ to a quantifier-free tautology. One purpose of this paper is to provide a description which in certain respects is more direct. Roughly speaking, ascent to A ⊃ A′ from a quantifier-free level will be replaced by movement from A to A′ on the quantificational level. Each movement will be closely related to the ascent it replaces.The new description makes use of a set L of rules of inference, the L-rules. L is complete in the sense that, if A is a conjunction and A′ an alternation of first-order formulas in prenex normal form, and if A ⊃ A′ is valid, then A′ can be obtained from A by an L-deduction, i.e., by applications of L-rules only. The distinctive feature of L is that each L-rule possesses two characteristics which, especially in combination, are desirable. First, each L-rule yields only conclusions implied by the premisses.
On recursively enumerable and arithmetic models of set theory
Authors: Rabin Michael O. 
Published: May 2006

In this note we shall prove a certain relative recursiveness lemma concerning countable models of set theory (Lemma 5). From this lemma will follow two results about special types of such models.Kreisel [5] and Mostowski [6] have shown that certain (finitely axiomatized) systems of set theory, formulated by means of the ϵ relation and certain additional non-logical constants, do not possess recursive models. Their purpose in doing this was to construct consistent sentences without recursive models. As a first corollary of Lemma 5, we obtain a very simple proof, not involving any formal constructions within the system of the notions of truth and satisfiability, of an extension of the Kreisel-Mostowski theorems. Namely, set theory with the single non-logical constant ϵ does not possess any recursively enumerable model. Thus we get, as a side product, an easy example of a consistent sentence containing a single binary relation which does not possess any recursively enumerable model; this sentence being the conjunction of the (finitely many) axioms of set theory.
Finite Axiomatizability using additional predicates
Authors: Craig W. , Vaught R. L. 
Published: May 2006

By a theory we shall always mean one of first order, having finitely many non-logical constants. Then for theories with identity (as a logical constant, the theory being closed under deduction in first-order logic with identity), and also likewise for theories without identity, one may distinguish the following three notions of axiomatizability. First, a theory may be recursively axiomatizable, or, as we shall say, simply, axiomatizable. Second, a theory may be finitely axiomatizable using additional predicates (f. a.+), in the syntactical sense introduced by Kleene [9]. Finally, the italicized phrase may also be interpreted semantically. The resulting notion will be called s. f. a.+. It is closely related to the modeltheoretic notion PC introduced by Tarski [16], or rather, more strictly speaking, to PC∩ACδ.For arbitrary theories with or without identity, it is easily seen that s. f. a.+ implies f. a.+ and it is known that f. a.+ implies axiomatizability. Thus it is natural to ask under what conditions the converse implications hold, since then the notions concerned coincide and one can pass from one to the other.Kleene [9] has shown: (1) For arbitrary theories without identity, axiomatizability implies f. a.+. It also follows from his work that : (2) For theories with identity which have only infinite models, axiomatizability implies f. a.+.
Der Prädikatenkalkül mit limitierten variablen Grundlegung einer natürlichen exakten Logik
Authors: Behmann Heinrich 
Published: May 2006

1. ÜberblickEine auf neue Art und mit neuen symbolischen Mitteln durchgeführte Analyse des Prozesses der Prädikation ergibt, daβ das für die logisch-mengentheoretischen Paradoxa nach Art des Russellschen essentielle Moment weder das der Selbstprädikation als solches ist noch irgendetwas, was man anderweitig bisher für sie verantwortlich gemacht hat, sondern vielmehr der Umstand, daβ der Algorithmus der Prädikation ebensowohl wie zu einem natürlichen Abschluβ auch auf einen unendlichen Regreβ führen kann. Damit werden die genannten Paradoxa als den bekannten erledigten der mathematischen unendlichen Prozesse wesentlich gleichartig und der gleichen Behandlung zugänglich erkannt. Das neue Kalkülmittel der limitierten Variablen bewirkt – ohne irgendwelche metalogische Regulative ad hoc – die automatische Sicherung des logischen Kalküls gegen die früheren Verführungen.
Short-Term Exposure to Fine Particulate Matter and Nitrogen Dioxide and Mortality in 4 Countries
Authors: Ma Yiqun , Nobile Federica , Marb Anne , Dubrow Robert , Stafoggia Massimo , Breitner Susanne , Kinney Patrick L. , Chen Kai 
Published: March 2024

ImportanceThe association between short-term exposure to air pollution and mortality has been widely documented worldwide; however, few studies have applied causal modeling approaches to account for unmeasured confounders that vary across time and space.ObjectiveTo estimate the association between short-term changes in fine particulate matter (PM2.5) and nitrogen dioxide (NO2) concentrations and changes in daily all-cause mortality rates using a causal modeling approach.Design, Setting, and ParticipantsThis cross-sectional study used air pollution and mortality data from Jiangsu, China; California; central-southern Italy; and Germany with interactive fixed-effects models to control for both measured and unmeasured spatiotemporal confounders. A total of 8 963 352 deaths in these 4 regions from January 1, 2015, to December 31, 2019, were included in the study. Data were analyzed from June 1, 2021, to October 30, 2023.ExposureDay-to-day changes in county- or municipality-level mean PM2.5 and NO2 concentrations.Main Outcomes and MeasuresDay-to-day changes in county- or municipality-level all-cause mortality rates.ResultsAmong the 8 963 352 deaths in the 4 study regions, a 10-μg/m3 increase in daily PM2.5 concentration was associated with an increase in daily all-cause deaths per 100 000 people of 0.01 (95% CI, 0.001-0.01) in Jiangsu, 0.03 (95% CI, 0.004-0.05) in California, 0.10 (95% CI, 0.07-0.14) in central-southern Italy, and 0.04 (95% CI, 0.02- 0.05) in Germany. The corresponding increases in mortality rates for a 10-μg/m3 increase in NO2 concentration were 0.04 (95% CI, 0.03-0.05) in Jiangsu, 0.03 (95% CI, 0.01-0.04) in California, 0.10 (95% CI, 0.05-0.15) in central-southern Italy, and 0.05 (95% CI, 0.04-0.06) in Germany. Significant effect modifications by age were observed in all regions, by sex in Germany (eg, 0.05 [95% CI, 0.03-0.06] for females in the single-pollutant model of PM2.5), and by urbanicity in Jiangsu (0.07 [95% CI, 0.04-0.10] for rural counties in the 2-pollutant model of NO2).Conclusions and RelevanceThe findings of this cross-sectional study contribute to the growing body of evidence that increases in short-term exposures to PM2.5 and NO2 may be associated with increases in all-cause mortality rates. The interactive fixed-effects model, which controls for unmeasured spatial and temporal confounders, including unmeasured time-varying confounders in different spatial units, can be used to estimate associations between changes in short-term exposure to air pollution and changes in health outcomes.
Educational Mobility, Pace of Aging, and Lifespan Among Participants in the Framingham Heart Study
Authors: Graf Gloria H. J. , Aiello Allison E. , Caspi Avshalom , Kothari Meeraj , Liu Hexuan , Moffitt Terrie E. , Muennig Peter A. , Ryan Calen P. , Sugden Karen , Belsky Daniel W. 
Published: March 2024

ImportancePeople who complete more education live longer lives with better health. New evidence suggests that these benefits operate through a slowed pace of biological aging. If so, measurements of the pace of biological aging could offer intermediate end points for studies of how interventions to promote education will affect healthy longevity.ObjectiveTo test the hypothesis that upward educational mobility is associated with a slower pace of biological aging and increased longevity.Design, Setting, and ParticipantsThis prospective cohort study analyzed data from 3 generations of participants in the Framingham Heart Study: (1) the original cohort, enrolled beginning in 1948; (2) the Offspring cohort, enrolled beginning in 1971; and (3) the Gen3 cohort, enrolled beginning in 2002. A 3-generation database was constructed to quantify intergenerational educational mobility. Mobility data were linked with blood DNA-methylation data collected from the Offspring cohort in 2005 to 2008 (n = 1652) and the Gen3 cohort in 2009 to 2011 (n = 1449). Follow-up is ongoing. Data analysis was conducted from June 2022 to November 2023 using data obtained from the National Institutes of Health database of Genotypes and Phenotypes (dbGaP).ExposureEducational mobility was measured by comparing participants’ educational outcomes with those of their parents.Main Outcomes and MeasuresThe pace of biological aging was measured from whole-blood DNA-methylation data using the DunedinPACE epigenetic clock. For comparison purposes, the analysis was repeated using 4 other epigenetic clocks. Survival follow-up was conducted through 2019.ResultsThis study analyzed data from 3101 participants from the Framingham Heart Study; 1652 were in the Offspring cohort (mean [SD] age, 65.57 [9.22] years; 764 [46.2%] male) and 1449 were in the Gen3 cohort (mean [SD] age, 45.38 [7.83] years; 691 [47.7%] male). Participants who were upwardly mobile in educational terms tended to have slower pace of aging in later life (r = −0.18 [95% CI, −0.23 to −0.13]; P &amp;lt; .001). This pattern of association was similar across generations and held in within-family sibling comparisons. There were 402 Offspring cohort participants who died over the follow-up period. Upward educational mobility was associated with lower mortality risk (hazard ratio, 0.89 [95% CI, 0.81 to 0.98]; P = .01). Slower pace of aging accounted for approximately half of this association.Conclusions and RelevanceThis cohort study’s findings support the hypothesis that interventions to promote educational attainment may slow the pace of biological aging and promote longevity. Epigenetic clocks have potential as near-term outcome measures of intervention effects on healthy aging. Experimental evidence is needed to confirm findings.
Foot and Ankle Care by Podiatrists and Amputations in Patients With Diabetes and Kidney Failure
Authors: Tan Tze-Woei , Caldwell Bryan , Zhang Yi , Kshirsagar Onkar , Cotter Dennis J. , Brewer Thomas W. 
Published: March 2024

ImportancePatients with kidney failure have an increased risk of diabetes-related foot complications. The benefit of regular foot and ankle care in this at-risk population is unknown.ObjectiveTo investigate foot and ankle care by podiatrists and the outcomes of diabetic foot ulcers (DFUs) in patients with kidney failure.Design, Setting, and ParticipantsThis retrospective cohort study included Medicare beneficiaries with type 2 diabetes receiving dialysis who had a new DFU diagnosis. The analysis of the calendar year 2016 to 2019 data from the United States Renal Data System was performed on June 15, 2023, with subsequent updates on December 11, 2023.ExposuresFoot and ankle care by podiatrists during 3 months prior to DFU diagnosis.Main Outcomes and MeasuresThe outcomes were a composite of death and/or major amputation, as well as major amputation alone. Kaplan-Meier analysis was used to estimate 2 to 3 years of amputation-free survival. Foot and ankle care by podiatrists and the composite outcome was examined using inverse probability-weighted Cox regression, while competing risk regression models were used for the analysis of amputation alone.ResultsAmong the 14 935 adult patients with kidney failure and a new DFU (mean [SD] age, 59.3 [12.7] years; 35.4% aged ≥65 years; 8284 men [55.4%]; Asian, 2.7%; Black/African American, 35.0%; Hispanic, 17.7%; White, 58.5%), 18.4% (n = 2736) received care by podiatrists in the 3 months before index DFU diagnosis. These patients were older, more likely to be male, and have more comorbidities than those without prior podiatrist visits. Over a mean (SD) 13.5 (12.0)-month follow-up, 70% of those with podiatric care experienced death and/or major amputation, compared with 74% in the nonpodiatric group. Survival probabilities at 36 months were 26.3% vs 22.8% (P &amp;lt; .001, unadjusted Kaplan-Meier survival analysis). In multivariate regression analysis, foot and ankle care was associated with an 11% lower likelihood of death and/or amputation (hazard ratio [HR], 0.89 95% CI, 0.84-0.93) and a 9% lower likelihood of major amputation (above or below knee) (HR, 0.91; 95% CI, 0.84-0.99) than those who did not.Conclusions and RelevanceThe findings of this study suggest that patients with kidney failure at risk for DFUs who receive foot and ankle care from podiatrists may be associated with a reduced likelihood of diabetes-related amputations.
Role of Ascorbate Peroxidase in Ascorbate‐glutathione Pathway for Stress Tolerance
Authors: Pandey Saurabh , Gupta Kapil , Gupta Kiran , Singh Ravindra P. , Kumar Amit , Gaur Anjali , Panigrahi Jogeswar 
Published: March 2024

Abstract
Under both normal and stressful circumstances, plants produce reactive oxygen species (ROS). However, when environmental conditions are too unfavourable, excessive ROS is produced and the antioxidative defence mechanisms cannot handle the high amounts of ROS, which results in plant damage. The antioxidant defence system's enzymatic and non‐enzymatic components detoxify and scavenge ROS to lessen their harmful effects. The ascorbate‐glutathione (AsA‐GSH) route, also referred to as the Asada‐Halliwell pathway, entails four enzymes that are essential for the detoxification of ROS: AsA peroxidase (APX), dehydroascorbate reductase (DHAR), monodehydroascorbate reductase (MDHAR), and GSH reductase (GR). These enzymes work in conjunction with other plant defence mechanisms in addition to detoxifying ROS to shield plants from different abiotic stress‐related harms. Numerous studies on plants have shown that the up‐regulation or overexpression of these antioxidant enzyme genes enhances the AsA and GSH levels in response to abiotic stresses and helps plants to lower ROS levels. This article outlines the role of APX as a crucial enzyme in the AsA‐GSH pathway and the capacity of plants to withstand abiotic stress.