bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0
Authors: Shlapentokh Alexandra 
Published: December 2007

AbstractLetKbe a function field of one variable over a constant fieldCof finite transcendence degree over ℂ. LetM/Kbe a finite extension and letWbe a set of primes ofKsuch that all but finitely many primes ofWdo not split in the extensionM/K. Then there exists a setW′ofK-primes such that Hilbert's Tenth Problem is not decidable overOK,W′= {xϵK∣ordþx≥ 0, ∀þ ∉W′}, and the set (W′ ∖W)∪{W∖W′) is finite.LetKbe a function field of one variable over a constant fieldCfinitely generated over ℚ. LetM/Kbe a finite extension and letWbe a set of primes ofKsuch that all but finitely many primes ofWdo not split in the extensionM/Kand the degree of all the primes inWis bounded bybϵ ℕ. Then there exists a setW′ ofK-primes such that ℤ has a Diophantine definition overOK,W′, and the set (W′ ∖W)∪(W∖W′) is finite.
Generalised weak presentations
Authors: Shlapentokh Alexandra 
Published: December 2007

AbstractLet K be a computable field. Let ℱ be a collection of recursive functions over K, possibly including field operations. We investigate the following question. Given an r.e. degree . is there an injective map j : K → ℕ such that j(K) is of degree a and all the functions in ℱ are translated by restrictions of total recursive functions.
Indestructibility and the level-by-level agreement between strong compactness and supercompactness
Authors: Apter Arthur W. , Hamkins Joel David 
Published: December 2007

AbstractCan a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets. or less level-by-level agreement, such as requiring it only on measure one sets, then yes. it can.
Some results on permutation group isomorphism and categoricity
Authors: Pillay Anand , Schlatter Mark D. 
Published: December 2007

AbstractWe extend Morley's Theorem to show that if a theory is κ-p-categorical for some uncountable cardinal κ, it is uncountably categorical. We then discuss ω-p-categoricity and provide examples to show that similar extensions for the Baldwin-Lachlan and Lachlan Theorems are not possible.
Properties of forking in ω-free pseudo-algebraically closed fields
Authors: Chatzidakis Zoé 
Published: December 2007

The study of pseudo-algebraically closed fields (henceforth called PAC) started with the work of J. Ax on finite and pseudo-finite fields [1]. He showed that the infinite models of the theory of finite fields are exactly the perfect PAC fields with absolute Galois group isomorphic to , and gave elementary invariants for their first order theory, thereby proving the decidability of the theory of finite fields. Ax's results were then extended to a larger class of PAC fields by M. Jarden and U. Kiehne [21], and Jarden [19]. The final word on theories of PAC fields was given by G. Cherlin, L. van den Dries and A. Macintyre [10], see also results by Ju. Ershov [13], [14]. Let K be a PAC field. Then the elementary theory of K is entirely determined by the following data:• The isomorphism type of the field of absolute numbers of K (the subfield of K of elements algebraic over the prime field).• The degree of imperfection of K.• The first-order theory, in a suitable ω-sorted language, of the inverse system of Galois groups al(L/K) where L runs over all finite Galois extensions of K.They also showed that the theory of PAC fields is undecidable, by showing that any graph can be encoded in the absolute Galois group of some PAC field. It turns out that the absolute Galois group controls much of the behaviour of the PAC fields. I will give below some examples illustrating this phenomenon.
The theory of modules of separably closed fields 1
Authors: Dellunde Pilar , Delon Françoise , Point Françoise 
Published: December 2007

AbstractWe consider separably closed fields of characteristic p > 0 and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the p-component functions.
On the binding group in simple theories
Authors: Shami Ziv , Wagner Frank O. 
Published: December 2007

AbstractWe show that ifpis a real type which is almost internal in a formula φ in a simple theory, then there is a typep′ interalgebraic with a finite tuple of realizations ofp, which is generated overφ. Moreover, the group of elementary permutations ofp′ over all realizations ofφis type-definable.
Isolation and lattice embeddings
Authors: Wu Guohua 
Published: December 2007

AbstractSay that (a, d) is an isolation pair if a is a c.e. degree, d is a d.c.e. degree, a < d and a bounds all c.e. degrees below d. We prove that there are an isolation pair (a, d) and a c.e. degree c such that c is incomparable with a, d, and c cups d to o′, caps a to o. Thus, {o, c, d, o′} is a diamond embedding, which was first proved by Downey in [9]. Furthermore, combined with Harrington-Soare continuity of capping degrees, our result gives an alternative proof of N5 embedding.
Generalized r-cohesiveness and the arithmetical hierarchy: a correction to “Generalized cohesiveness”
Authors: Jockusch Carl G. , Lakins Tamara J. 
Published: December 2007

AbstractFor X ⊆ ω, let [X]n denote the class of all n-element subsets of X. An infinite set A ⊆ ω is called n-r-cohesive if for each computable function f: [ω]n → {0, 1} there is a finite set F such that f is constant on [A − F]n. We show that for each n > 2 there is no Πn0 set A ⊆ ω which is n-r-cohesive. For n = 2 this refutes a result previously claimed by the authors, and for n ≥ 3 it answers a question raised by the authors.
Strong convergence in finite model theory
Authors: Lotfallah Wafik Boulos 
Published: December 2007

AbstractIn [9] we introduced a new framework for asymptotic probabilities, in which a σ-additive measure is defined on the sample space of all sequences of finite models, where the universe of , is {1,2,…,n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in eventually almost surely or fails in eventually almost surely.In this paper we define the strong convergence law for formulas, which carries over the ideas of the strong 0-1 law to formulas with free variables, and roughly states that for each formula ϕ(x), the fraction of tuples a in , which satisfy the formula ϕ(x), almost surely has a limit as n tends to infinity.We show that the infinitary logic with finitely many variables has the strong convergence law for formulas for the uniform measure, and further characterize the measures on random graphs for which the strong convergence law holds.
The torsionfree part of the Ziegler spectrum of RG when R is a Dedekind domain and G is a finite group
Authors: Marcja A. , Prest M. , Toffalori C. 
Published: December 2007

For every ring S with identity, the (right) Ziegler spectrum of S, Zgs, is the set of (isomorphism classes of) indecomposable pure injective (right) S-modules. The Ziegler topology equips Zgs with the structure of a topological space. A typical basic open set in this topology is of the formwhere φ and ψ are pp-formulas (with at most one free variable) in the first order language Ls for S-modules; let [φ/ψ] denote the closed set Zgs - (φ/ψ). There is an alternative way to introduce the Ziegler topology on Zgs. For every choice of two f.p. (finitely presented) S-modules A, B and an S-module homomorphism f: A → B, consider the set (f) of the points N in Zgs such that some S-homomorphism h: A → N does not factor through f. Take (f) as a basic open set. The resulting topology on Zgs is, again, the Ziegler topology.The algebraic and model-theoretic relevance of the Ziegler topology is discussed in [Z], [P] and in many subsequent papers, including [P1], [P2] and [P3], for instance. Here we are interested in the Ziegler spectrum ZgRG of a group ring RG, where R is a Dedekind domain of characteristic 0 (for example R could be the ring Z of integers) and G is a finite group. In particular we deal with the R-torsionfree points of ZgRG.The main motivation for this is the study of RG-lattices (i.e., finitely generated R-torsionfree RG-modules).
On regular reduced products
Authors: Kennedy Juliette , Shelah Saharon 
Published: December 2007

AbstractAssume (ℵ0, ℵ1) → (λ, λ+). Assume M is a model of a first order theory T of cardinality at most λ+ in a language of cardinality ≤ λ. Let N be a model with the same language. Let Δ be a set of first order formulas in and let D be a regular filter on λ. Then M is Δ-embeddable into the reduced power Nλ/D, provided that every Δ-existential formula true in M is true also in N. We obtain the following corollary: for M as above and D a regular ultrafilter over λ, Mλ/D is λ++-universal. Our second result is as follows: For i < μ let Mi, and Ni, be elementarily equivalent models of a language which has cardinality ≤ λ. Suppose D is a regular filter on λ and (ℵ0, ℵ1) → (λ, λ+) holds. We show that then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ΠiMi/D and ΠiNi/D. This yields the following corollary: Assume GCH and λ regular (or just (ℵ0, ℵ1) → (λ, λ+) and 2λ = λ+. For L, Mi and Ni be as above, if D is a regular filter on λ, then ΠiMi/D ≅ ΠiNi/D.
Automorphism groups of models of Peano arithmetic
Authors: Schmerl James H. 
Published: December 2007

Which groups are isomorphic to automorphism groups of models of Peano Arithmetic? It will be shown here that any group that has half a chance of being isomorphic to the automorphism group of some model of Peano Arithmetic actually is.For any structure, let Aut() be its automorphism group. There are groups which are not isomorphic to any model= (N, +, ·, 0, 1, ≤) of PA. For example, it is clear that Aut(N), being a subgroup of Aut((, <)), must be torsion-free. However, as will be proved in this paper,if(A, <)is a linearly ordered set and G is a subgroup of Aut((A, <)),then there are modelsofPAsuch that Aut() ≅G.Ifis a structure, then its automorphism group can be considered as a topological group by letting the stabilizers of finite subsets ofAbe the basic open subgroups. If′ is an expansion of, then Aut(′) is a closed subgroup of Aut(). Conversely, for any closed subgroupG≤ Aut() there is an expansion′ ofsuch that Aut(′) =G. Thus, ifis a model of PA, then Aut() is not only a subgroup of Aut((N, <)), but it is even aclosedsubgroup of Aut((N, ′)).There is a characterization, due to Cohn [2] and to Conrad [3], of those groupsGwhich are isomorphic to closed subgroups of automorphism groups of linearly ordered sets.
IKP and friends
Authors: Lubarsky Robert S. 
Published: December 2007

There has been increasing interest in intuitionistic methods over the years. Still, there has been relatively little work on intuitionistic set theory, and most of that has been on intuitionistic ZF. This investigation is about intuitionistic admissibility and theories of similar strength.There are several more particular goals for this paper. One is just to get some more Kripke models of various set theories out there. Those papers that have dealt with IZF usually were more proof-theoretic in nature, and did not provide models. Furthermore, the inspirations for many of the constructions here are classical forcing arguments. Although the correspondence between the forcing and the Kripke constructions is not made tight, the relationship between these two methods is of interest (see [6] for instance) and some examples, even if only suggestive, should help us better understand the relationship between forcing and Kripke constructions. Along different lines, the subject of least and greatest fixed points of inductive definitions, while of interest to computer scientists, has yet to be studied constructively, and probably holds some surprises. Admissibility is of course the proper set-theoretic context for this study. Finally, while most of the classical material referred to here has long been standard, some of it has not been well codified and may even be unknown, so along the way we'll even fill in a gap in the classical literature.The next section develops the basics of IKP, including some remarks on fixed points of inductive definitions.
Cardinalities in the projective hierarchy
Authors: Hjorth Greg 
Published: December 2007

We show that the “effective cardinality” of the collection of sets is strictly bigger than the effective cardinality of the . The phrase effective cardinality is vague but can be made exact in the usual ways. For instance:Theorem 1.1. Assume ADL(ℝ)Then in L(ℝ) there is no injection.A few years ago Tony Martin showed a similar result, establishing the non-existence of an injection from to for m sufficiently larger than n. His method did not seem to work for m = n + 1.This present paper gives level by level calculations for the projective hierarchy, but it too falls short of a complete analysis, in as much as it leaves the position of the effective cardinals in the Wadge degrees largely obscure. At the low levels it takes some time for any new cardinals to appear. Whenever Γ1, Γ2 are non-trivial Wadge degrees strictly included in one has.
Splitting and nonsplitting, II: A low2 c.e. degree above which 0′ is not splittable
Authors: Cooper S. Barry , Li Angsheng 
Published: December 2007

AbstractIt is shown that there exists a low2 Harrington non-splitting base — that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if 0′ = x ∨ y, then either 0′ = x ∨ a or 0′ = y ∨ a. Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the low2-ness requirements to be satisfied, and the proof given involves new techniques with potentially wider application.
On iterating semiproper preorders
Authors: Miyamoto Tadatoshi 
Published: December 2007

AbstractLet T be an ω1-Souslin tree. We show the property of forcing notions; “is {ω1}-semi-proper and preserves T” is preserved by a new kind of revised countable support iteration of arbitrary length. As an application we have a forcing axiom which is compatible with the existence of an ω1 -Souslin tree for preorders as wide as possible.
A rank for the class of elementary submodels of a superstable homogeneous model
Authors: Hyttinen Tapani , Lessmann Olivier 
Published: December 2007

AbstractWe study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any dependence relation for superstable homogeneous models.
A constructive look at the completeness of the space (ℝ)
Authors: Ishihara Hajime , Yoshida Satoru 
Published: December 2007

AbstractWe show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space (ℝ) of test functions is equivalent to the principle BD-ℕ which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.
Modulated fibring and the collapsing problem
Authors: Sernadas Cristina , Rasga João , Carnielli Walter A. 
Published: December 2007

AbstractFibring is recognized as one of the main mechanisms in combining logics, with great significance in the theory and applications of mathematical logic. However, an open challenge to fibring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that fibring imposes unwanted interconnections between the given logics. Modulated fibring allows a finer control of the combination, solving the collapsing problem both at the semantic and deductive levels. Main properties like soundness and completeness are shown to be preserved, comparison with fibring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem.
Borovik-Poizat rank and stability
Authors: Burdges Jeffrey , Cherlin Gregory 
Published: December 2007

Borovik proposed an axiomatic treatment of Morley rank in groups, later modified by Poizat, who showed that in the context of groups the resulting notion of rank provides a characterization of groups of finite Morley rank [2]. (This result makes use of ideas of Lascar, which it encapsulates in a neat way.) These axioms form the basis of the algebraic treatment of groups of finite Morley rank undertaken in [1].There are, however, ranked structures, i.e., structures on which a Borovik-Poizat rank function is defined, which are not ℵ0-stable [1, p. 376]. In [2, p. 9] Poizat raised the issue of the relationship between this notion of rank and stability theory in the following terms: “… ungroupede Borovik est une structure stable, alors qu'un univers rangé n'a aucune raison de l'être …” (emphasis added). Nonetheless, we will prove the following:Theorem 1.1.A ranked structure is superstable.An example of a non-ℵ0-stable structure with Borovik-Poizat rank 2 is given in [1, p. 376]. Furthermore, it appears that this example can be modified in a straightforward way to give ℵ0-stable structures of Borovik-Poizat rank 2 in which the Morley rank is any countable ordinal (which would refute a claim of [1, p. 373, proof of C.4]). We have not checked the details. This does not leave much room for strenghthenings of our theorem. On the other hand, the proof of Theorem 1.1 does give a finite bound for the heights of certain trees of definable sets related to unsuperstability, as we will see in Section 5.
Contiguity and distributivity in the enumerable Turing degrees — Corrigendum
Authors: Downey Rodney G. , Lempp Steffen 
Published: December 2007

A computably enumerable Turing degree a is called contiguous iff it contains only a single computably enumerable weak truth table degree (Ladner and Sasso [2]). In [1], the authors proved that a nonzero computably enumerable degree a is contiguous iff it is locally distributive, that is, for all a1, a2, c with a1 ∪a2 = a and c ≤ a, there exist ci, ≤ ai with c1 ∪ c2 = c.To do this we supposed that W was a computably enumerable set and ∪ a computably set with a Turing functional Φ such that ΦW = U. Then we constructed computably enumerable sets A0, A1 and B together with functionals Γ0, Γ1, Γ, and Δ so thatand so as to satisfy all the requirements below.That is, we built a degree-theoretical splitting A0, A1 of W and a set B ≤TW such that if we cannot beat all possible degree-theoretical splittings V0, V1 of B then we were able to witness the fact that U ≤WW (via Λ).After the proof it was observed that the set U of the proof (page 1222, paragraph 4) needed only to be Δ20. It was then claimed that a consequence to the proof was that every contiguous computably enumerable degree was, in fact, strongly contiguous, in the sense that all (not necessarily computably enumerable) sets of the degree had the same weak truth table degree.
Group configurations and germs in simple theories
Authors: Ben-Yaacov Itay 
Published: December 2007

AbstractWe develop the theory of germs of generic functions in simple theories. Starting with an algebraic quadrangle (or other similar hypotheses), we obtain an “almost” generic group chunk, where the product is defined up to a bounded number of possible values. This is the first step towards the proof of the group configuration theorem for simple theories, which is completed in [3].
Interaction Between Certain Moulds and Aflatoxin B1 Producer Aspergillus Flavus NRRL 3251
Authors: Cvetnić Zdenka , Pepeljnjak Stjepan 
Published: December 2007

Interaction Between Certain Moulds and Aflatoxin B1ProducerAspergillus FlavusNRRL 3251The objective of this study was to evaluate biotic interaction between some mould species and active producer of aflatoxin B1Aspergillus flavusNRRL 3251, co-cultured in yeast-extract sucrose (YES) broth. Twenty-five mould strains ofAlternariaspp.,Cladosporiumspp.,Mucorspp.,A. flavusandA. niger, used as biocompetitive agents, were isolated from outdoor and indoor airborne fungi, scrapings of mouldy household walls, and from stored and post-harvest maize. Aflatoxin B1was extracted from mould biomasses with chloroform and detected using the multitoxin TLC method. The results confirm antagonistic interaction between all strains tested. WithAlternariaspp. andCladosporiumspp., aflatoxin B1production decreased 100 %, compared to detection in a single culture ofA. flavusNRRL 3251 (Cmean=18.7 μg mL-1). In mixed cultures withMucorspp., aflatoxinB1levels dropped to (5.6-9.3) μg mL-1, and the inhibition was from 50 % to 70 %. Four of five aflatoxin non-producing strains ofA. flavusinterfered with aflatoxin production in mixed culture, and reduced AFB1productivity by 100 %. One strain showed a lower efficacy in inhibiting AFB1production (80 %) with a detectable amount of AFB13.7 μg mL-1when compared to control. A decrease in toxin production was also observed in dual cultivation withA. nigerstrains. It resulted in 100 % reduction in three strains), 90 % reduction in one strain (Cmean=1.9 μg mL-1) and 80 % reduction in one strain (Cmean=3.7 μg mL-1) inhibition.
Endocrinological and Behavioural Effects of Chronic Fluxilan Administration in Rats
Authors: Spasojević Nataša , Gavrilović Ljubica , Kovačević Ivan , Dronjak Slađana 
Published: December 2007

Endocrinological and Behavioural Effects of Chronic Fluxilan Administration in RatsChronic stress induces changes in the neuroendocrine and neuronal system, including elevation of catecholamines and corticosterone (CORT) levels, and could be an important factor in initial depression. Antidepressants affect monoaminergic neurotransmission and modulate central neuropeptides involved in the coordination of stress response and the control of HPA axis activity. We studied the effects of chronic treatment with fluxilan, a selective inhibitor of serotonin reuptake, in unstressed controls and chronic unpredictable mild stress (CUMS) rats, on behaviour and plasma noradrenaline (NA), adrenaline (A), corticosterone (CORT) and adrenocorticotropic hormone (ACTH). CUMS did not affect plasma NA, A and ACTH, but elevated plasma CORT content. Plasma concentration of catecholamines after fluxilan administration was significantly increased in control and CUMS group. On the other hand, fluxilan expressed no effect on plasma ACTH and CORT concentrations in control animals, but decreased ACTH and CORT levels in CUMS animals. Behaviourally, fluxilan treated animals displayed enhanced anxiety. The results demonstrate that the anxiogenic effects of chronic fluxilan administration are similar to those reported by many other studies. The findings described here suggest that elevated plasma catecholamines may contribute to an adverse effect of this drug on cardiovascular parameters during antidepressant therapy.