bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the convergence of query-bounded computations and logical closure properties of c.e. sets
Authors: McNicholl Timothy H. 
Published: May 2006

Abstract.Call a set A n-correctable if every set Turing reducible to A via a Turing machine that on any input makes at most n queries is Turing reducible to A via a Turing machine that on any input makes at most n-queries and on any input halts no matter what answers are given to its queries. We show that if a c.e. set A is n-correctable for some n ≥ 2, then it is n-correctable for all n. We show that this is the optimal such result by constructing a c.e. set that is 1-correctable but not 2-correctable. The former result is obtained by examining the logical closure properties of c.e. sets that are 2-correctable.
Implication with possible exceptions
Authors: Jurjus Herman , de Swart Harrie 
Published: May 2006

AbstractWe introduce an implication-with-possible-exceptions and define validity of rules-with-possible-exceptions by means of the topological notion of a full subset. Our implication-with-possible-exceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other hand, modus ponens and the rule of monotony, as well as all other laws of classical propositional logic, are valid-up-to-possible exceptions. As a consequence, the rules of classical propositional logic do not determine the meaning of deducibility and inference as implication-without-exceptions.
Finite variable logic, stability and finite models
Authors: Djordjević Marko 
Published: May 2006

We will study complete Ln-theories and their models, where Ln is the set of first order formulas in which at most n distinct variables occur. Here, by a complete Ln-theory we mean a theory such that for every Ln-sentence, it or its negation is implied by the theory. Hence, a complete Ln-theory need not necessarily be complete in the usual sense. Our approach is to transfer concepts and methods from stability theory, such as the order property and counting types, to the context of Ln-theories. So, in one sense, we will develop some rudimentary stability theory for a particular class of (possibly) incomplete theories. To make the ‘stability theoretic’ arguments work, we need to assume that models of the complete Ln-theory T which we consider can be amalgamated in certain ways. If this condition is satisfied and T has infinite models then there will exist models of T which are sufficiently saturated with respect to Ln. This allows us to use some counting types arguments from stability theory. If, moreover, we impose some finiteness conditions on the number of Ln-types and the length of Ln-definable orders then a sufficiently saturated model of T will be ω-categorical and ω-stable. Using the theory of ω-categorical and ω-stable structures we derive that T has arbitrarily large finite models.A different approach to combining stability theory with finite model theory is made by Hyttinen in [9] and [10].
A note on equational theories
Authors: Junker Markus 
Published: May 2006

Several attempts have been done to distinguish “positive” information in an arbitrary first order theory, i.e., to find a well behaved class of closed sets among the definable sets. In many cases, a definable set is said to be closed if its conjugates are sufficiently distinct from each other. Each such definition yields a class of theories, namely those where all definable sets are constructible, i.e., boolean combinations of closed sets. Here are some examples, ordered by strength:Weak normality describes a rather small class of theories which are well understood by now (see, for example, [P]). On the other hand, normalization is so weak that all theories, in a suitable context, are normalizable (see [HH]). Thus equational theories form an interesting intermediate class of theories. Little work has been done so far. The original work of Srour [S1, S2, S3] adopts a point of view that is closer to universal algebra than to stability theory. The fundamental definitions and model theoretic properties can be found in [PS], though some easy observations are missing there. Hrushovski's example of a stable non-equational theory, the first and only one so far, is described in the unfortunately unpublished manuscript [HS]. In fact, it is an expansion of the free pseudospace constructed independently by Baudisch and Pillay in [BP] as an example of a strictly 2-ample theory. Strong equationality, defined in [Hr], is also investigated in [HS].
Actions of non-compact and non-locally compact Polish groups
Authors: Solecki Sławomir 
Published: May 2006

AbstractWe show that each non-compact Polish group admits a continuous action on a Polish space with non-smooth orbit equivalence relation. We actually construct a free such action. Thus for a Polish group compactness is equivalent to all continuous free actions of this group being smooth. This answers a question of Kechris. We also establish results relating local compactness of the group with its inability to induce orbit equivalence relations not reducible to countable Borel equivalence relations. Generalizing a result of Hjorth, we prove that each non-locally compact, that is, infinite dimensional, separable Banach space has a continuous action on a Polish space with non-Borel orbit equivalence relation, thus showing that this property characterizes non-local compactness among Banach spaces.
Stable theories with a new predicate
Authors: Casanovas Enrique , Ziegler Martin 
Published: May 2006

Let M be an L-structure and A be an infinite subset of M. Two structures can be defined from A:• The induced structure on A has a name Rφ for every ∅-definable relation φ(M) ∩ An on A. Its language isA with its Lind-structure will be denoted by Aind.• The pair (M, A) is an L(P)-structure, where P is a unary predicate for A and L(P) = L ∪{P}.We call A small if there is a pair (N, B) elementarily equivalent to (M, A) and such that for every finite subset b of N every L–type over Bb is realized in N.A formula φ(x, y) has the finite cover property (f.c.p) in M if for all natural numbers k there is a set of φ–formulaswhich is k–consistent but not consistent in M. M has the f.c.p if some formula has the f.c.p in M. It is well known that unstable structures have the f.c.p. (see [6].) We will prove the following two theorems.Theorem A. Let A be a small subset of M. If M does not have the finite cover property then, for every λ ≥ ∣L∣, if both M andAindare λ–stable then (M, A) is λ–stable.Corollary 1.1 (Poizat [5]). If M does not have the finite cover property and N ≺ M is a small elementary substructure, then (M, N) is stable.Corollary 1.2 (Zilber [7]). If U is the group of wots of unity in the field ℂ of complex numbers the pair (ℂ, U) isω–stable.Proof. (See [4].) As a strongly minimal set ℂ is ω–stable and does not have the f.c.p. By the subspace theorem of Schmidt [3] every algebraic set intersects U in a finite union of translates of subgroups definable in the group structure of U alone. Whence Uind is nothing more than a (divisible) abelian group, which is ω–stable.
An investigation on the logical structure of mathematics (V). Contradictions of Russell's type
Authors: Kuroda Sigekatu 
Published: May 2006

If a contradiction is deduced by using only the defining formula of a set, it is called a contradiction of Russell's type, and the set is called inconsistent. A set is called consistent, if no contradiction can be deduced from the defining formula of the set.The object of this note is to determine some conditions for some sets to be consistent or inconsistent.In §1 notations and terms are defined. In §2 main results are stated. In §3, the proof in UL of a contradiction is simplified for a special kind of sets, so that a simplified definition of the proof of a contradiction is given for the kind of sets, and some properties of a proof in UL are stated concerning the simplified definition. This definition and the properties of a proof are the basis of the proof of the results given in §§5–10. Thus, this Part (V), except §3, is written independently of other Parts as far as possible. However, it depends essentially on Parts (I) and (II). In §4 some examples are given.
Entailment and relevance1
Authors: Belnap Nuel D. 
Published: May 2006

Those who object to the identification of strict implication and entail-ment speak in such a way that for A to entail B, A must be relevant to B. This view of entailment agrees not only with that of the naive student of logic (who tends to think the phrase paradoxes of “implication” more accurate than “paradoxes” of implication), but also with that expressed in the initial chapters of many textbooks in logic under the heading “Fallacies of Relevance.”2In regard to formal theories proposed as explications of the notion of entailment, it becomes important to have at our disposal some formal account of the demand for relevance as between antecedent and consequent of an entailment.
Note on Carnap's relational asymptotic relative frequencies
Authors: Harary Frank 
Published: May 2006

A (binary) relation is a collection of ordered couples. Two relations are isomorphic if there is a 1–1 correspondence between their fields which preserves the ordered couples. Isomorphism between relations is itself an equivalence relation, and a structure is an isomorphism class of binary relations.Carnap ([1], p. 124) asks certain questions concerning (both the exact and) the asymptotic value of the relative frequency that a relation on p objects satisfies certain properties. Among the most interesting special cases are the asymptotic value of the relative frequency that a binary relation on p objects be (a) symmetric, (b) reflexive, (c) transitive irreflexive anti-symmetric, and (d) symmetric irreflexive. These results already appear either in, or almost in, the literature, in various disguises. The object of this expository note is to bring them to light, especially since some of the references may not be generally known to logicians.Carnap ([1], p. 124) points out explicitly the correspondence between binary relations and linear graphs. Davis [2] and Harary [4] obtains precise results for the number of structures with certain properties using the language of relations and graphs respectively; but these do not supply the asymptotic values directly. The asymptotic results which are most useful here are either contained in, or are straight-forward extensions of, the formulas presented in Ford and Uhlenbeck [3], which in turn are based on unpublished work of G. Pólya. In addition, we utilize a result of L. Moser on transitive relations, which appears in Wine and Freund [5].
Corrections to a theory of restricted quantification
Authors: Hailperin Theodore 
Published: May 2006

R. Sherman Lehman has called my attention to an error which vitiates the proofs of two theorems in the paper mentioned in the title (this Journal, vol. 22, pp. 19–35, 113–129). New proofs are here presented.Proof of Lemma, p. 27. Induction Step: Assume as hypothesis of induction that the lemma holds for formulas P with n—1 or fewer free restricted variables and consider a P having n (n>0) such variables.
Peirce's axioms for propositional calculus
Authors: Prior A. N. 
Published: May 2006

In 1885 Peirce axiomatised the propositional calculus on the basis of five ‘icons’ or axioms, which with Cpq for ‘If p then q’ and o for a false proposition, and with the source in Peirce's [2] beside each, may be represented as follows: 1. Cpp (3.376); 2. CCpCqrCqCpr (3.377); 3. CCpqCCqrCpr (3.379); 4. Cop (3.381); 5. CCCpqpp (3.384). From these Peirce proves, among other things, 6. CpCCpqq (3.377), 7. CpCqp (3.378), and with Np (Not p) for Cpo, 8. CNNpp (3.384).By a well-known result of Wajsberg's II. 93, the entire two-valued propositional calculus is derivable by substitution and detachment from 3, 4, 5, and 7 (with Df. N). In Berry [1] this is taken to show the completeness of Peirce's basis; but this proof will not do as it stands. For Peirce's proof of 7 consists in first passing from 1 to CqCpp by the argument that ‘to say that (x ⥽ x) is generally true is to say that it is so in every state of things, say in that in which y is true’; and then from CqCpp to 7 by 2. This procedure clearly involves, formally, the use not only of substitution and detachment but of a rule to infer ⊦ Cqα. from ⊦α. Peirce's basis is sufficient with substitution and detachment nevertheless; for by a less well-known result of Wajsberg's II. 93, 3, 4, 5, and 6 are sufficient in this sense, and Peirce does prove 6 by substitution and detachment from 1 and 2.
Reductions of Hilbert's tenth problem
Authors: Davis Martin , Putnam Hilary 
Published: May 2006

Hilbert's tenth problem is to find an algorithm for determining whether or not a diophantine equation possesses solutions. A diophantine predicate (of positive integers) is defined to be one of the formwhere P is a polynomial with integral coefficients (positive, negative, or zero). Previous work has considered the variables as ranging over nonnegative integers; but we shall find it more useful here to restrict the range to positive integers, no essential change being thereby introduced. It is clear that the recursive unsolvability of Hilbert's tenth problem would follow if one could show that some non-recursive predicate were diophantine. In particular, it would suffice to show that every recursively enumerable predicate is diophantine. Actually, it would suffice to prove far less.
On the definition of an infinitely-many-valued predicate calculus
Authors: Rutledge Joseph D. 
Published: May 2006

This paper presents a class of plausible definitions for validity of formulas in the infinitely-many-valued extension of the Łukasiewicz predicate calculus, and shows that all of them are equivalent. This extended system is discussed in some form in [3] and [4]; the questions discussed here are raised rather briefly in the latter.We first describe the formal framework for the validity definition. The symbols to be used are the following: the connectives + and ‐, which are the strong disjunction B of [2] and negation respectively; the predicate variables Pi for i ∈ I, where I may be taken as the integers; the existential quantifiers E(J), where J⊆I, and I may be thought of as the index set on the individual variables, which however do not appear explicitly in this formulation.
Subbarrel patterns of thalamocortical innervation in rat somatosensory cortical barrels: Organization and postnatal development
Authors: Louderback Katherine M. , Glass Christina S. , Shamalla‐Hannah Lorraine , Erickson Susan L. , Land Peter W. 
Published: May 2006

AbstractBarrel hollows in the posteromedial barrel subfield of adult rat somatosensory cortex typically encompass two or three metabolically and structurally distinct regions, termed subbarrels. We used immunohistochemical staining for vesicular glutamate transporter 2 and the neuronal serotonin transporter, in conjunction with cytochrome oxidase (CO) histochemistry, to investigate the distribution of thalamocortical (TC) axon terminals in relation to subbarrel domains. We found, first, that CO‐dark subbarrels are more intensely immunoreactive for thalamocortical terminals than the CO‐light clefts that separate them. Second, during the first postnatal week, immunoreactivity for markers of TC terminals is relatively homogeneous throughout the barrel hollow; subbarrel patterns of distribution only become recognizable between P‐8 and P‐10. These observations extend previous findings that subbarrels denote barrel regions enriched in synaptic contacts. The data also indicate that allocation of TC terminals into subbarrel domains does not occur immediately upon thalamic axon ingrowth. Instead, refinement of TC arbors into subbarrels is a gradual process, the outcome of which is not manifest until the second week of postnatal life. J. Comp. Neurol. 497:32–41, 2006. © 2006 Wiley‐Liss, Inc.
Physics and Politics—an Old Analogy Revised
Authors: Munro William Bennett 
Published: May 2006

It is just fifty-five years since Walter Bagehot wrote his Physics and Politics, a very suggestive book in its day. He began the first chapter of this book with a reference to “the sudden acquisition of much physical knowledge” which had marked the second half of the nineteenth century, and declared it his purpose to show the bearing of these new ideks upon the political conceptions of mankind. That purpose he, fulfilled with much ingenuity, pointing out the various lines along which the advance in natural science seemed to suggest modifications in the old theories of the state and of government.This was only a half-century ago; yet the new physics of Bagehot's day has already growh old. Its basic concepts have been turned inside out and upside down. Its laws relating to the indestructibility of mass and the conservation of energy have been radically amended. Even a generation ago the atom was held to be the ultimate and indivisible unit in the composition of the universe. It was the basis upon which the scientists of the nineteenth century built up an inclusive set of laws and principles relating to the structure of all creation. No one had ever seen an atom, but its existence could be postulated and its properties were held to be knowable.
Latin America and the League of Nations
Authors: Martin Percy Alvin 
Published: May 2006

To students of international relations it has become almost a commonplace that among the most significant and permanent results of the World War has been the changed international status of the republics of Latin America. As a result of the war and post-war developments in these states, the traditional New World isolation in South America, as well as in North America, is a thing of the past. To our leading sister republics is no longer applicable the half-contemptuous phrase, current in the far-off days before 1914, that Latin America stands on the margin of international life. The new place in the comity of nations won by a number of these states is evidenced—to take one of the most obvious examples—by the raising of the legations of certain non-American powers to the rank of embassies, either during or immediately after the war. In the case of Brazil, for instance, where prior to 1914 only the United States maintained an ambassador, at the present time Great Britain, France, Italy, Belgium, Portugal, and Japan maintain diplomatic representatives of this rank.Yet all things considered one of the most fruitful developments in the domain of international relations has been the share taken by our southern neighbors in the work of the League of Nations. All of the Latin American republics which severed relations with Germany or declared war against that country were entitled to participate in the Peace Conference. As a consequence, eleven of these states affixed their signatures to the Treaty of Versailles, an action subsequently ratified in all cases except Ecuador.
Constitutional Law in 1924–1925: The Constitutional Decisions of the Supreme Court of the United States in the October Term, 1924
Authors: Cushman Robert E. 
Published: May 2006

The decisions arising under the commerce clause of the Constitution during the 1924 term of the Supreme Court did not involve any striking extension of national authority in that field. There was no case approaching in significance the Recapture Clause Case decided in the previous term. However, the reinforcement of a familiar principle through a striking application of it, or the lucid and pungent expression of an old doctrine, lends some significance to several cases which otherwise have no far-reaching importance.In the case of Brooks v. United States the court sustained the constitutionality of the National Motor Vehicle Theft Act of 1919. The act subjected to heavy penalties any one who transported or caused to be transported in interstate or foreign commerce any motor vehicle, knowing it to have been stolen, and any one who, with the same guilty knowledge, “shall receive, conceal, store, barter, sell, or dispose of any motor vehicle, moving as, or which is a part of, or which constitutes interstate or foreign commerce.” It is certainly no surprise to learn from the opinion of Chief Justice Taft that the power to regulate commerce which is broad enough to enable Congress to bar from interstate transportation lottery tickets, diseased cattle, adulterated food, prize-fight films, and the like, and to penalize the interstate transportation of women for immoral purposes, is a power which can likewise be used to punish those who abuse the privileges of interstate and foreign commerce by using them in the furtherance of larceny or the disposal of stolen goods.
The Delimitation and Mensurability of Political Phenomena
Authors: Catlin George E. G. 
Published: May 2006

Political science is not a sociological science of everything, a psychological study of all human behavior in all aspects, an anthropological inquiry into miscellaneous human customs, or a philosophy of history. Still less is it a study only of the state, which is a form of social organization resulting from one species of political action, or a study only of governments and the stage properties of law and administration.Politics is concerned with a field of human behavior characterized by the recurrence of specific behavior patterns. These peculiarly political patterns, however, must not be treated simply as a series of incidents in mere temporal juxtaposition. Human history must be studied as natural history and physical phenomena have been studied, that is to say, with a view to the detection of a recurrence in these patterns, and, hence, of a process in accordance with which, in given total situations, given detailed behavior patterns recur. These patterns are “lines of conduct” of an individual or group character, pursued in relation to other individuals or groups, as a matter of human method in dealing with such situations, which situations arise partly from the nature of the non-human environment, partly from the historical combination of human factors. The resultant specific action or behavior recurs with the recurrence of the stimuli of the approximately recurrent situation; for example, a certain general situation known as “the outbreak of hostilities” has certain specific consequences in changes of individual conduct toward members of a given nation, and the need of putting through a domestic policy against opposition brings into play the ever similar methods of party organization.