共查询到20条相似文献,搜索用时 46 毫秒
1.
Alexander P. Kreuzer 《Mathematical Logic Quarterly》2014,60(3):177-183
We show how one can obtain solutions to the Arzelà‐Ascoli theorem using suitable applications of the Bolzano‐Weierstraß principle. With this, we can apply the results from 10 and obtain a classification of the strength of instances of the Arzelà‐Ascoli theorem and a variant of it. Let be the statement that each equicontinuous sequence of functions contains a subsequence that converges uniformly with the rate and let be the statement that each such sequence contains a subsequence which converges uniformly but possibly without any rate. We show that is instance‐wise equivalent, over , to the Bolzano‐Weierstraß principle and that is instance‐wise equivalent, over , to , and thus to the strong cohesive principle (). Moreover, we show that over the principles , and are equivalent. 相似文献
2.
Pierre Matet 《Mathematical Logic Quarterly》2014,60(4-5):246-265
Our main results are: (A) It is consistent relative to a large cardinal that holds but fails. (B) If holds and are two infinite cardinals such that and λ carries a good scale, then holds. (C) If are two cardinals such that κ is λ‐Shelah and , then there is no good scale for λ. 相似文献
3.
We develop an approach to the longstanding conjecture of Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η‐like computable linear ordering , such that has no interval of order type η, and such that the order type of is determined by a ‐limitwise monotonic maximal block function, there exists computable such that has no nontrivial automorphism. 相似文献
4.
Longyun Ding 《Mathematical Logic Quarterly》2014,60(4-5):273-279
In this paper, notions of ‐like and c0‐like equivalence relations are introduced. We characterize the positions of ‐like and c0‐like equivalence relations in the Borel reducibility hierarchy by comparing them with equivalence relations and . 相似文献
5.
Locally finite ω‐languages and effective analytic sets have the same topological complexity
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Olivier Finkel 《Mathematical Logic Quarterly》2016,62(4-5):303-318
Local sentences and the formal languages they define were introduced by Ressayre in 28 . We prove that locally finite ω‐languages and effective analytic sets have the same topological complexity: the Borel and Wadge hierarchies of the class of locally finite ω‐languages are equal to the Borel and Wadge hierarchies of the class of effective analytic sets. In particular, for each non‐null recursive ordinal there exist some ‐complete and some ‐complete locally finite ω‐languages, and the supremum of the set of Borel ranks of locally finite ω‐languages is the ordinal , which is strictly greater than the first non‐recursive ordinal . This gives an answer to the question of the topological complexity of locally finite ω‐languages, which was asked by Simonnet 30 and also by Duparc, Finkel, and Ressayre in 5 . Moreover we show that the topological complexity of a locally finite ω‐language defined by a local sentence φ may depend on the models of the Zermelo‐Fraenkel axiomatic system . Using similar constructions as in the proof of the above results we also show that the equivalence, the inclusion, and the universality problems for locally finite ω‐languages are ‐complete, hence highly undecidable. 相似文献
6.
Irakli Chitaia 《Mathematical Logic Quarterly》2016,62(6):590-595
We prove that the c.e. Q1‐degrees are not dense, and there exists a c.e. Q1‐degree with no minimal c.e. predecessors. It is proved that if M1 and M2 are maximal sets such that then or . We also show that there exist infinite collections of Q1‐degrees and such that the following hold: (i) for every , , , and , (ii) each consists entirely of maximal sets; and (iii) each consists entirely of non‐maximal hyperhypersimple sets. 相似文献
7.
On the set‐theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements
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In set theory without the Axiom of Choice , we study the deductive strength of the statements (“Every partially ordered set without a maximal element has two disjoint cofinal subsets”), (“Every partially ordered set without a maximal element has a countably infinite disjoint family of cofinal subsets”), (“Every linearly ordered set without a maximum element has two disjoint cofinal subsets”), and (“Every linearly ordered set without a maximum element has a countably infinite disjoint family of cofinal subsets”). Among various results, we prove that none of the above statements is provable without using some form of choice, is equivalent to , + (Dependent Choices) implies , does not imply in (Zermelo‐Fraenkel set theory with the Axiom of Extensionality modified in order to allow the existence of atoms), does not imply in (Zermelo‐Fraenkel set theory minus ) and (hence, ) is strictly weaker than in . 相似文献
8.
Eleftherios Tachtsis 《Mathematical Logic Quarterly》2016,62(3):190-203
Martin's Axiom is the statement that for every well‐ordered cardinal , the statement holds, where is “if is a c.c.c. quasi order and is a family of dense sets in P, then there is a ‐generic filter of P”. In , the fragment is provable, but not in general in . In this paper, we investigate the interrelation between and various choice principles. In the choiceless context, it makes sense to drop the requirement that the cardinal κ be well‐ordered, and we can define for any (not necessarily well‐ordered) cardinal the statement to be “if is a c.c.c. quasi order with , and is a family of dense sets in P, then there is a ‐generic filter of P”. We then define to be the statement that for every (not necessarily well‐ordered) cardinal , we have that holds. We then investigate the set‐theoretic strength of the principle . 相似文献
9.
Tristan Kuijpers 《Mathematical Logic Quarterly》2015,61(3):151-158
In this paper, we prove a definable version of Kirszbraun's theorem in a non‐Archimedean setting for definable families of functions in one variable. More precisely, we prove that every definable function , where and , that is λ‐Lipschitz in the first variable, extends to a definable function that is λ‐Lipschitz in the first variable. 相似文献
10.
Working with uncountable structures of fixed cardinality, we investigate the complexity of certain equivalence relations and show that if , then many of them are ‐complete, in particular the isomorphism relation of dense linear orders. Then we show that it is undecidable in whether or not the isomorphism relation of a certain well behaved theory (stable, NDOP, NOTOP) is ‐complete (it is, if , but can be forced not to be). 相似文献
11.
Mirjana Ilić 《Mathematical Logic Quarterly》2016,62(6):465-480
In this paper, we give a sequent calculus for the positive contraction‐less relevant logic and we give a proof that it is cut‐free without the use of the truth constant t. Based on , we re‐prove the decidability of the logic . 相似文献
12.
Jan Šaroch 《Mathematical Logic Quarterly》2015,61(3):196-201
We prove that the property characterizes Σ‐algebraically compact modules if is not ω‐measurable. Moreover, under a large cardinal assumption, we show that over any ring R where is not ω‐measurable, any free module M of ω‐measurable rank satisfies , hence the assumption on cannot be dropped in general (e.g., over small non‐right perfect rings). In this way, we extend results from a recent paper by Simion Breaz 4 . 相似文献
13.
Rod Downey Carl Jockusch Timothy H. McNicholl Paul Schupp 《Mathematical Logic Quarterly》2015,61(3):189-195
We classify the asymptotic densities of the sets according to their level in the Ershov hierarchy. In particular, it is shown that for , a real is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any . 相似文献
14.
Norihiro Kamide 《Mathematical Logic Quarterly》2016,62(6):552-562
A paraconsistent modal‐like logic, , is defined as a Gentzen‐type sequent calculus. The modal operator in the modal logic can be simulated by the paraconsistent double negation in . Some theorems for embedding into a Gentzen‐type sequent calculus for and vice versa are proved. The cut‐elimination and completeness theorems for are also proved. 相似文献
15.
Suppose that P is a forcing notion, L is a language (in ), a P‐name such that “ is a countable L‐structure”. In the product , there are names such that for any generic filter over , and . Zapletal asked whether or not implies that there is some such that . We answer this question negatively and discuss related issues. 相似文献
16.
Norihiro Kamide 《Mathematical Logic Quarterly》2016,62(3):177-189
In this paper, the positive fragment of the logic of contraction‐less relevant implication is extended with the addition of a paraconsistent negation connective similar to the strong negation connective in Nelson's paraconsistent four‐valued logic . This extended relevant logic is called , and it has the property of constructible falsity which is known to be a characteristic property of . A Gentzen‐type sequent calculus for is introduced, and the cut‐elimination and decidability theorems for are proved. Two extended Routley‐Meyer semantics are introduced for , and the completeness theorems with respect to these semantics are proved. 相似文献
17.
Toshimichi Usuba 《Mathematical Logic Quarterly》2016,62(1-2):59-71
We study the subtlety of a cardinal κ and of . We show that, under a certain large cardinal assumption, it is consistent that is subtle for some but κ is not subtle, and the consistency of such a situation is much stronger than the existence of a subtle cardinal. We show that the subtlety of can be characterized by a certain partition relation on . We also study the property of faintness of κ, and the subtlety of with the strong inclusion. 相似文献
18.
Yong Cheng 《Mathematical Logic Quarterly》2015,61(4-5):329-340
In this paper we characterize the strong reflecting property for ‐cardinals for all , characterize Harrington's Principle and its generalization and discuss the relationship between the strong reflecting property for ‐cardinals and Harrington's Principle . 相似文献
19.
Athanassios Tzouvaras 《Mathematical Logic Quarterly》2015,61(1-2):103-116
Let be a countable first‐order language and be an ‐structure. “Definable set” means a subset of M which is ‐definable in with parameters. A set is said to be immune if it is infinite and does not contain any infinite definable subset. X is said to be partially immune if for some definable A, is immune. X is said to be totally non‐immune if for every definable A, and are not immune. Clearly every definable set is totally non‐immune. Here we ask whether the converse is true and prove that it is false for every countable structure whose class of definable sets satisfies a mild condition. We investigate further the possibility of an alternative construction of totally non‐immune non‐definable sets with the help of a subclass of immune sets, the class of cohesive sets, as well as with the help of a generalization of definable sets, the semi‐definable ones (the latter being naturally defined in models of arithmetic). Finally connections are found between totally non‐immune sets and generic classes in nonstandard models of arithmetic. 相似文献
20.
Rami Grossberg Monica VanDieren Andrés Villaveces 《Mathematical Logic Quarterly》2016,62(4-5):367-382
We prove the following main theorem: Let be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality μ. Let μ be a cardinal above the the Löwenheim‐Skolem number of the class. If is μ‐Galois‐stable, has no μ‐Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two ‐limits over M, for , are isomorphic over M. 相似文献