Annals of Pure and Applied Logic最新文献

Completeness in local positive logic 局部正逻辑中的完备性

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-04-08 DOI: 10.1016/j.apal.2025.103601

Arturo Rodríguez Fanlo , Ori Segel

引用次数: 0

The Set-Cover game and non-measurable unions Set-Cover游戏和不可衡量的工会

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-04-07 DOI: 10.1016/j.apal.2025.103602

Taras Banakh , Robert Rałowski , Szymon Żeberski

引用次数: 0

Some more results on relativized Chaitin's Ω 关于相对化柴廷的Ω的更多结果

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-04-04 DOI: 10.1016/j.apal.2025.103586

Liang Yu

引用次数: 0

Generics in invariant subsets of the group of order preserving permutations of Q Q的保序置换群的不变子集中的泛型

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-03-25 DOI: 10.1016/j.apal.2025.103585

M. Drzewiecka , A. Ivanov , B. Mokry

引用次数: 0

Extender-based Magidor-Radin forcings without top extenders 基于扩展器的Magidor-Radin强制装置，无需顶部扩展器

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-03-21 DOI: 10.1016/j.apal.2025.103584

Moti Gitik , Sittinon Jirattikansakul

引用次数: 0

Upward Löwenheim-Skolem-Tarski numbers for abstract logics 向上Löwenheim-Skolem-Tarski数字抽象逻辑

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-03-19 DOI: 10.1016/j.apal.2025.103583

Victoria Gitman , Jonathan Osinski

{"title":"Upward Löwenheim-Skolem-Tarski numbers for abstract logics","authors":"Victoria Gitman , Jonathan Osinski","doi":"10.1016/j.apal.2025.103583","DOIUrl":"10.1016/j.apal.2025.103583","url":null,"abstract":"<div><div>Galeotti, Khomskii and Väänänen recently introduced the notion of the upward Löwenheim-Skolem-Tarski number for a logic, strengthening the classical notion of a Hanf number. A cardinal κ is the upward Löwenheim-Skolem-Tarski number (ULST number) of a logic <math><mi>L</mi></math> if it is the least cardinal with the property that whenever M is a model of size at least κ satisfying a sentence φ in <math><mi>L</mi></math>, then there are arbitrarily large models satisfying φ and having M as a substructure. The substructure requirement is what differentiates the ULST number from the Hanf number and gives the notion large cardinal strength. While it is a theorem of ZFC that every logic has a Hanf number, Galeotti, Khomskii and Väänänen showed that the existence of the ULST number for second-order logic implies the existence of a partially extendible cardinal. We answer positively their conjecture that the ULST number for second-order logic is the least extendible cardinal.</div><div>We define the strong ULST number by strengthening the substructure requirement to elementary substructure. We investigate the ULST and strong ULST numbers for several classical strong logics: infinitary logics, the equicardinality logic, logic with the well-foundedness quantifier, second-order logic, and sort logics. We show that the ULST and the strong ULST numbers are characterized in some cases by classical large cardinals and in some cases by natural new large cardinal notions that they give rise to. We show that for some logics the notions of the ULST number, strong ULST number and least strong compactness cardinal coincide, while for others, it is consistent that they can be separated. Finally, we introduce a natural large cardinal notion characterizing strong compactness cardinals for the equicardinality logic.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103583"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Piecewise convex embeddability on linear orders 线性阶上的分段凸嵌入性

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-03-13 DOI: 10.1016/j.apal.2025.103581

Martina Iannella , Alberto Marcone , Luca Motto Ros , Vadim Weinstein

{"title":"Piecewise convex embeddability on linear orders","authors":"Martina Iannella , Alberto Marcone , Luca Motto Ros , Vadim Weinstein","doi":"10.1016/j.apal.2025.103581","DOIUrl":"10.1016/j.apal.2025.103581","url":null,"abstract":"<div><div>Given a nonempty set <math><mi>L</mi></math> of linear orders, we say that the linear order L is <math><mi>L</mi></math>-convex embeddable into the linear order <math><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup></math> if it is possible to partition L into convex sets indexed by some element of <math><mi>L</mi></math> which are isomorphic to convex subsets of <math><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup></math> ordered in the same way. This notion generalizes convex embeddability and (finite) piecewise convex embeddability (both studied in [13]), which are the special cases <math><mi>L</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>}</mo></math> and <math><mi>L</mi><mo>=</mo><mrow><mi>Fin</mi></mrow></math>. We focus mainly on the behavior of these relations on the set of countable linear orders, first characterizing when they are transitive, and hence a quasi-order. We then study these quasi-orders from a combinatorial point of view, and analyze their complexity with respect to Borel reducibility. Finally, we extend our analysis to uncountable linear orders.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103581"},"PeriodicalIF":0.6,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Cardinal characteristics on bounded generalised Baire spaces 有界广义Baire空间上的基数特征

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-03-12 DOI: 10.1016/j.apal.2025.103582

Tristan van der Vlugt

引用次数: 0

P-measures in models without P-points 没有p点的模型中的p测度

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-03-10 DOI: 10.1016/j.apal.2025.103579

Piotr Borodulin-Nadzieja , Jonathan Cancino-Manríquez , Adam Morawski

引用次数: 0

A complete invariant system for noetherian BL-algebras and more general L-algebras noether bl -代数和更一般的l -代数的完全不变系统

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2025-03-07 DOI: 10.1016/j.apal.2025.103580

Wolfgang Rump

{"title":"A complete invariant system for noetherian BL-algebras and more general L-algebras","authors":"Wolfgang Rump","doi":"10.1016/j.apal.2025.103580","DOIUrl":"10.1016/j.apal.2025.103580","url":null,"abstract":"<div><div>Main results on BL-algebras, including their classification in the finite case, are reconsidered and extended to a class of L-algebras X with prime factorization, including BL-algebras with ascending chain condition for its lattice. The weighted forest associated with a finite BL-algebra reappears as a canonical L-subalgebra <math><mover><mrow><mi>P</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>X</mi><mo>)</mo></math> of prime elements in the self-similar closure <math><mi>S</mi><mo>(</mo><mi>X</mi><mo>)</mo></math> where <math><mover><mrow><mi>P</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>X</mi><mo>)</mo></math> is completely determined by its underlying poset (not necessarily a forest), while the weights are associated with existing powers of the prime elements in X. These invariants determine X within its self-similar closure <math><mi>S</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mi>S</mi><mo>(</mo><mover><mrow><mi>P</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math>. The three basic types of BL-algebras are related to concepts of L-algebras with further-reaching significance in quantum theory.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 7","pages":"Article 103580"},"PeriodicalIF":0.6,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0