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Annals of Pure and Applied Logic最新文献

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Good projective witnesses 好的投影证人
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2025-08-01 Epub Date: 2025-05-05 DOI: 10.1016/j.apal.2025.103606
Vera Fischer , Sy David Friedman , David Schrittesser , Asger Törnquist
{"title":"Good projective witnesses","authors":"Vera Fischer ,&nbsp;Sy David Friedman ,&nbsp;David Schrittesser ,&nbsp;Asger Törnquist","doi":"10.1016/j.apal.2025.103606","DOIUrl":"10.1016/j.apal.2025.103606","url":null,"abstract":"<div><div>We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality <span><math><msub><mrow><mi>a</mi></mrow><mrow><mtext>g</mtext></mrow></msub></math></span> of a maximal cofinitary group (MCG) is strictly between <span><math><msub><mrow><mi>ℵ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><mi>c</mi></math></span>, and there is a <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>-definable MCG of this cardinality. Here <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> is optimal, making this result a natural counterpart to the Borel MCG of Horowitz and Shelah. Our theorem has its analogue in the realm of maximal almost disjoint (MAD) families, extending a line of results regarding the definability properties of MAD families in models with large continuum.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103606"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143927371","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
Unreachability of Γ2n+1,m 无法到达Γ2n+1，m
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2025-08-01 Epub Date: 2025-04-23 DOI: 10.1016/j.apal.2025.103604
Derek Levinson
{"title":"Unreachability of Γ2n+1,m","authors":"Derek Levinson","doi":"10.1016/j.apal.2025.103604","DOIUrl":"10.1016/j.apal.2025.103604","url":null,"abstract":"<div><div>We find bounds for the maximal length of a sequence of distinct <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>2n</mn><mo>+</mo><mn>1</mn><mo>,</mo><mi>m</mi></mrow></msub></math></span>-sets under <em>AD</em> and show there is no sequence of distinct <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>2n</mn><mo>+</mo><mn>1</mn></mrow></msub></math></span>-sets of length <span><math><msubsup><mrow><mi>δ</mi></mrow><mrow><mn>2n</mn><mo>+</mo><mn>3</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>. As a special case, there is no sequence of distinct <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>m</mi></mrow></msub></math></span>-sets of length <span><math><msub><mrow><mi>ℵ</mi></mrow><mrow><mi>m</mi><mo>+</mo><mn>2</mn></mrow></msub></math></span>. These are the optimal results for the pointclasses <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>2n</mn><mo>+</mo><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>m</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103604"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895035","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
Indestructible supercompactness and level by level inequivalence 不可摧毁的超紧性和逐级的不等价
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2025-08-01 Epub Date: 2025-05-30 DOI: 10.1016/j.apal.2025.103618
Arthur W. Apter
{"title":"Indestructible supercompactness and level by level inequivalence","authors":"Arthur W. Apter","doi":"10.1016/j.apal.2025.103618","DOIUrl":"10.1016/j.apal.2025.103618","url":null,"abstract":"<div><div>We construct via forcing a model for the level by level inequivalence between strong compactness and supercompactness containing a fully indestructible supercompact cardinal. This answers a question posed at the end of <span><span>[2]</span></span> and <span><span>[6]</span></span>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103618"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204601","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
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 : 2025-08-01 Epub 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 ,&nbsp;Alberto Marcone ,&nbsp;Luca Motto Ros ,&nbsp;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 <span><math><mi>L</mi></math></span> of linear orders, we say that the linear order <em>L</em> is <span><math><mi>L</mi></math></span>-convex embeddable into the linear order <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> if it is possible to partition <em>L</em> into convex sets indexed by some element of <span><math><mi>L</mi></math></span> which are isomorphic to convex subsets of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> ordered in the same way. This notion generalizes convex embeddability and (finite) piecewise convex embeddability (both studied in <span><span>[13]</span></span>), which are the special cases <span><math><mi>L</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>}</mo></math></span> and <span><math><mi>L</mi><mo>=</mo><mrow><mi>Fin</mi></mrow></math></span>. 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":"2025-08-01","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
Descriptive complexity of topological invariants 拓扑不变量的描述复杂性
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2025-08-01 Epub Date: 2025-05-14 DOI: 10.1016/j.apal.2025.103611
Djamel Eddine Amir, Mathieu Hoyrup
{"title":"Descriptive complexity of topological invariants","authors":"Djamel Eddine Amir,&nbsp;Mathieu Hoyrup","doi":"10.1016/j.apal.2025.103611","DOIUrl":"10.1016/j.apal.2025.103611","url":null,"abstract":"<div><div>In this article, we investigate the descriptive complexity of topological invariants. Our main goal is to understand the expressive power of low complexity invariants, by investigating which spaces they can distinguish. We study the invariants in the first two levels of the Borel hierarchy. We develop techniques to establish whether two spaces can be separated by invariants in these levels. We show that they are sufficient to separate finite topological graphs. We finally identify the complexity of recognizing the line segment.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103611"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068773","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
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 : 2025-08-01 Epub Date: 2025-03-25 DOI: 10.1016/j.apal.2025.103585
M. Drzewiecka , A. Ivanov , B. Mokry
{"title":"Generics in invariant subsets of the group of order preserving permutations of Q","authors":"M. Drzewiecka ,&nbsp;A. Ivanov ,&nbsp;B. Mokry","doi":"10.1016/j.apal.2025.103585","DOIUrl":"10.1016/j.apal.2025.103585","url":null,"abstract":"<div><div>Let <span><math><mi>ρ</mi><mo>∈</mo><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mo>&lt;</mo><mo>)</mo></math></span> and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>ρ</mi></mrow></msub></math></span> be the closure of the conjugacy class of <em>ρ</em> in <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mo>&lt;</mo><mo>)</mo></math></span>. We show that <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>ρ</mi></mrow></msub></math></span> contains a conjugacy class, say <em>C</em>, which is comeagre in <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>ρ</mi></mrow></msub></math></span>. We describe representatives of <em>C</em>. Furthermore, we show that the family of finite partial maps extendable to elements of <em>C</em> has the cofinal amalgamation property.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103585"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799916","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
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 : 2025-08-01 Epub Date: 2025-04-04 DOI: 10.1016/j.apal.2025.103586
Liang Yu
{"title":"Some more results on relativized Chaitin's Ω","authors":"Liang Yu","doi":"10.1016/j.apal.2025.103586","DOIUrl":"10.1016/j.apal.2025.103586","url":null,"abstract":"<div><div>We prove that, assuming ZF, and restricted to any <span><math><msub><mrow><mo>≤</mo></mrow><mrow><mi>T</mi></mrow></msub></math></span>-pointed set, Chaitin's <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>U</mi></mrow></msub><mo>:</mo><mi>x</mi><mo>↦</mo><msubsup><mrow><mi>Ω</mi></mrow><mrow><mi>U</mi></mrow><mrow><mi>x</mi></mrow></msubsup><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><msup><mrow><mi>U</mi></mrow><mrow><mi>x</mi></mrow></msup><mo>(</mo><mi>σ</mi><mo>)</mo><mo>↓</mo></mrow></msub><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mo>|</mo><mi>σ</mi><mo>|</mo></mrow></msup></math></span> is not injective for any universal prefix-free Turing machine <em>U</em>, and that <span><math><msubsup><mrow><mi>Ω</mi></mrow><mrow><mi>U</mi></mrow><mrow><mi>x</mi></mrow></msubsup></math></span> fails to be degree invariant in a very strong sense, answering several recent questions in descriptive set theory. Moreover, we show that under <span><math><mrow><mi>ZF</mi></mrow><mo>+</mo><mrow><mi>AD</mi></mrow></math></span>, every function <em>f</em> mapping <em>x</em> to <em>x</em>-random must be uncountable-to-one over an upper cone of Turing degrees.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103586"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816774","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
Interpolation in Hájek's basic logic 插值在Hájek的基本逻辑
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2025-08-01 Epub Date: 2025-05-26 DOI: 10.1016/j.apal.2025.103615
Wesley Fussner , Simon Santschi
{"title":"Interpolation in Hájek's basic logic","authors":"Wesley Fussner ,&nbsp;Simon Santschi","doi":"10.1016/j.apal.2025.103615","DOIUrl":"10.1016/j.apal.2025.103615","url":null,"abstract":"<div><div>We exhaustively classify varieties of BL-algebras with the amalgamation property, showing that there are only countably many of them and solving an open problem of Montagna. As a consequence of this classification, we obtain a complete description of which axiomatic extensions of Hájek's basic fuzzy logic <strong>BL</strong> have the deductive interpolation property. Along the way, we provide similar classifications of varieties of basic hoops with the amalgamation property and axiomatic extensions of the negation-free fragment of <strong>BL</strong> with the deductive interpolation property.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103615"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147947","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
Equational definitions of logical filters 逻辑滤波器的等式定义
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2025-08-01 Epub Date: 2025-05-28 DOI: 10.1016/j.apal.2025.103617
Michele Pra Baldi , Adam Přenosil
{"title":"Equational definitions of logical filters","authors":"Michele Pra Baldi ,&nbsp;Adam Přenosil","doi":"10.1016/j.apal.2025.103617","DOIUrl":"10.1016/j.apal.2025.103617","url":null,"abstract":"<div><div>A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by translating logical rules directly into equations. The former type of algebraic interpretation has been extensively studied and underlies the theory of algebraization, whereas little systematic attention has been paid to the latter type. We investigate a semantic form of the latter type of algebraic interpretation, which we call the equational definability of compact filters (EDCF). Paralleling the well-studied hierarchy of variants of the deduction–detachment theorem (DDT), this property also comes in local, parametrized, and parametrized local variants. The main results of this paper characterize of each of these variants of the EDCF in a spirit similar to the existing characterizations of the DDT. While the EDCF hierarchy and the DDT hierarchy coincide for algebraizable logics, part of the interest of the EDCF stems from the fact it is often enjoyed even by logics which are not well-behaved in terms of other existing classifications in algebraic logic.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103617"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170698","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
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 : 2025-08-01 Epub Date: 2025-04-07 DOI: 10.1016/j.apal.2025.103602
Taras Banakh , Robert Rałowski , Szymon Żeberski
{"title":"The Set-Cover game and non-measurable unions","authors":"Taras Banakh ,&nbsp;Robert Rałowski ,&nbsp;Szymon Żeberski","doi":"10.1016/j.apal.2025.103602","DOIUrl":"10.1016/j.apal.2025.103602","url":null,"abstract":"<div><div>Using a game-theoretic approach we present a generalization of the classical result of Brzuchowski, Cichoń, Grzegorek and Ryll-Nardzewski on non-measurable unions. We also present applications of obtained results to Marczewski–Burstin representable ideals.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103602"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808427","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
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