Annals of Pure and Applied Logic最新文献

{"title":"Topological games in Ramsey spaces","authors":"Julián C. Cano ,&nbsp;Carlos A. Di Prisco","doi":"10.1016/j.apal.2025.103630","DOIUrl":"10.1016/j.apal.2025.103630","url":null,"abstract":"<div><div>Topological Ramsey theory studies a class of combinatorial topological spaces, known as topological Ramsey spaces, unifying the essential features of those combinatorial frames where the Ramsey property is equivalent to the Baire property. In this article, we present a general overview of the combinatorial structure of topological Ramsey spaces and their main properties, and we propose an alternative proof of the abstract Ellentuck theorem for a large family of axiomatized topological Ramsey spaces. Additionally, we introduce the notion of selective axiomatized topological Ramsey space, and generalize Kastanas games in order to characterize the Ramsey property for this broad family of topological Ramsey spaces through topological games.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 10","pages":"Article 103630"},"PeriodicalIF":0.6,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144514036","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}

{"title":"Unstable independence from the categorical point of view","authors":"Mark Kamsma ,&nbsp;Jiří Rosický","doi":"10.1016/j.apal.2025.103629","DOIUrl":"10.1016/j.apal.2025.103629","url":null,"abstract":"<div><div>We give a category-theoretic construction of simple and NSOP₁-like independence relations in locally finitely presentable categories, and in the more general locally finitely multipresentable categories. We do so by identifying properties of a class of monomorphisms <span><math><mi>M</mi></math></span> such that the pullback squares consisting of morphisms in <span><math><mi>M</mi></math></span> form the desired independence relation. This generalizes the category-theoretic construction of stable independence relations using effective unions or cellular squares by M. Lieberman, S. Vasey and the second author to the unstable setting.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 10","pages":"Article 103629"},"PeriodicalIF":0.6,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322319","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}

{"title":"An explicit Kuznetsov-Muravitsky enrichment","authors":"Mamuka Jibladze,&nbsp;Evgeny Kuznetsov","doi":"10.1016/j.apal.2025.103628","DOIUrl":"10.1016/j.apal.2025.103628","url":null,"abstract":"<div><div>An embedding of arbitrary Heyting algebra <em>H</em> into a reduct from the variety of Kuznetsov-Muravitsky algebras is constructed. An algebraic proof is given that this reduct belongs to the variety of Heyting algebras generated by <em>H</em>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 10","pages":"Article 103628"},"PeriodicalIF":0.6,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144364463","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}

{"title":"Automorphisms of P(ω)/fin and large continuum","authors":"Alan Dow","doi":"10.1016/j.apal.2025.103627","DOIUrl":"10.1016/j.apal.2025.103627","url":null,"abstract":"<div><div>We prove that it is consistent with <span><math><mi>c</mi><mo>&gt;</mo><msub><mrow><mi>ℵ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> that all automorphisms of <span><math><mi>P</mi><mo>(</mo><mi>ω</mi><mo>)</mo><mo>/</mo><mtext>fin</mtext></math></span> are trivial.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 10","pages":"Article 103627"},"PeriodicalIF":0.6,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263932","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}

{"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":"2025-05-30","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}

{"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":"2025-05-28","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}

{"title":"The singleton degrees of the Σ20 sets are not dense","authors":"Thomas F. Kent ,&nbsp;Keng Meng Ng ,&nbsp;Andrea Sorbi","doi":"10.1016/j.apal.2025.103616","DOIUrl":"10.1016/j.apal.2025.103616","url":null,"abstract":"<div><div>Answering an open question raised by Cooper, we show that there exist <span><math><msubsup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> sets <em>D</em> and <em>E</em> such that the singleton degree of <em>E</em> is a minimal cover of the singleton degree of <em>D</em>. This shows that the <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> singleton degrees, and the <span><math><msubsup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> singleton degrees, are not dense (and consequently the <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> <em>Q</em>-degrees, and the <span><math><msubsup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> <em>Q</em>-degrees, are not dense). Moreover, <em>D</em> and <em>E</em> can be built to lie in the same enumeration degree.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103616"},"PeriodicalIF":0.6,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195893","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}

{"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":"2025-05-26","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}

{"title":"Model-theoretic K1 of free modules over PIDs","authors":"Sourayan Banerjee,&nbsp;Amit Kuber","doi":"10.1016/j.apal.2025.103613","DOIUrl":"10.1016/j.apal.2025.103613","url":null,"abstract":"<div><div>Motivated by Krajiček and Scanlon's definition of the Grothendieck ring <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>M</mi><mo>)</mo></math></span> of a first-order structure <em>M</em>, we introduce the definition of <em>K</em>-groups <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>M</mi><mo>)</mo></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>0</mn></math></span> via Quillen's <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>S</mi></math></span> construction. We provide a recipe for the computation of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> is a free module over a PID <em>R</em>, subject to the knowledge of the abelianizations of the general linear groups <span><math><mi>G</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. As a consequence, we provide explicit computations of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></math></span> when <em>R</em> belongs to a large class of Euclidean domains that includes fields with at least 3 elements and polynomial rings over fields with characteristic 0. We also show that the algebraic <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of a PID <em>R</em> embeds into <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103613"},"PeriodicalIF":0.6,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116947","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}

{"title":"The power of the Binary Value Principle","authors":"Yaroslav Alekseev ,&nbsp;Edward A. Hirsch","doi":"10.1016/j.apal.2025.103614","DOIUrl":"10.1016/j.apal.2025.103614","url":null,"abstract":"<div><div>The (extended) Binary Value Principle (<span><math><mi>eBVP</mi></math></span>, the equation <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><msup><mrow><mn>2</mn></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mo>−</mo><mi>k</mi></math></span> for <span><math><mi>k</mi><mo>&gt;</mo><mn>0</mn></math></span> and Boolean variables <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>) has received a lot of attention recently, several lower bounds have been proved for it <span><span>[1]</span></span>, <span><span>[2]</span></span>, <span><span>[11]</span></span>. Also it has been shown <span><span>[1]</span></span> that the probabilistically verifiable Ideal Proof System (<span><math><mi>IPS</mi></math></span>) <span><span>[8]</span></span> together with <span><math><mi>eBVP</mi></math></span> polynomially simulates a similar semialgebraic proof system. In this paper we consider Polynomial Calculus with an algebraic version of Tseitin's extension rule (<span><math><mrow><mi>Ext</mi></mrow><mtext>-</mtext><mrow><mi>PC</mi></mrow></math></span>) that introduces a new variable for any polynomial. Contrary to <span><math><mi>IPS</mi></math></span>, this is a Cook–Reckhow proof system. We show that in this context <span><math><mi>eBVP</mi></math></span> still allows to simulate similar semialgebraic systems. We also prove that it allows to simulate the Square Root Rule <span><span>[6]</span></span>, which is in sharp contrast with the result of <span><span>[2]</span></span> that shows an exponential lower bound on the size of <span><math><mrow><mi>Ext</mi></mrow><mtext>-</mtext><mrow><mi>PC</mi></mrow></math></span> derivations of the Binary Value Principle from its square. On the other hand, we demonstrate that <span><math><mi>eBVP</mi></math></span> probably does not help in proving exponential lower bounds for Boolean formulas: we show that an <span><math><mrow><mi>Ext</mi></mrow><mtext>-</mtext><mrow><mi>PC</mi></mrow></math></span> (even with the Square Root Rule) derivation of any unsatisfiable Boolean formula in CNF from <span><math><mi>eBVP</mi></math></span> must be of exponential size.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103614"},"PeriodicalIF":0.6,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195892","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}