Pub Date : 2025-05-30DOI: 10.1016/j.apal.2025.103618
Arthur W. Apter
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 [2] and [6].
{"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}
Pub Date : 2025-05-28DOI: 10.1016/j.apal.2025.103617
Michele Pra Baldi , Adam Přenosil
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.
{"title":"Equational definitions of logical filters","authors":"Michele Pra Baldi , 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}
Pub Date : 2025-05-27DOI: 10.1016/j.apal.2025.103616
Thomas F. Kent , Keng Meng Ng , Andrea Sorbi
Answering an open question raised by Cooper, we show that there exist sets D and E such that the singleton degree of E is a minimal cover of the singleton degree of D. This shows that the singleton degrees, and the singleton degrees, are not dense (and consequently the Q-degrees, and the Q-degrees, are not dense). Moreover, D and E can be built to lie in the same enumeration degree.
{"title":"The singleton degrees of the Σ20 sets are not dense","authors":"Thomas F. Kent , Keng Meng Ng , 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}
Pub Date : 2025-05-26DOI: 10.1016/j.apal.2025.103615
Wesley Fussner , Simon Santschi
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 BL 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 BL with the deductive interpolation property.
{"title":"Interpolation in Hájek's basic logic","authors":"Wesley Fussner , 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}
Pub Date : 2025-05-22DOI: 10.1016/j.apal.2025.103613
Sourayan Banerjee, Amit Kuber
Motivated by Krajiček and Scanlon's definition of the Grothendieck ring of a first-order structure M, we introduce the definition of K-groups for via Quillen's construction. We provide a recipe for the computation of , where is a free module over a PID R, subject to the knowledge of the abelianizations of the general linear groups . As a consequence, we provide explicit computations of when R 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 of a PID R embeds into .
{"title":"Model-theoretic K1 of free modules over PIDs","authors":"Sourayan Banerjee, 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}
Pub Date : 2025-05-21DOI: 10.1016/j.apal.2025.103614
Yaroslav Alekseev , Edward A. Hirsch
The (extended) Binary Value Principle (, the equation for and Boolean variables ) has received a lot of attention recently, several lower bounds have been proved for it [1], [2], [11]. Also it has been shown [1] that the probabilistically verifiable Ideal Proof System () [8] together with polynomially simulates a similar semialgebraic proof system. In this paper we consider Polynomial Calculus with an algebraic version of Tseitin's extension rule () that introduces a new variable for any polynomial. Contrary to , this is a Cook–Reckhow proof system. We show that in this context still allows to simulate similar semialgebraic systems. We also prove that it allows to simulate the Square Root Rule [6], which is in sharp contrast with the result of [2] that shows an exponential lower bound on the size of derivations of the Binary Value Principle from its square. On the other hand, we demonstrate that probably does not help in proving exponential lower bounds for Boolean formulas: we show that an (even with the Square Root Rule) derivation of any unsatisfiable Boolean formula in CNF from must be of exponential size.
{"title":"The power of the Binary Value Principle","authors":"Yaroslav Alekseev , 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>></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}
Pub Date : 2025-05-14DOI: 10.1016/j.apal.2025.103611
Djamel Eddine Amir, Mathieu Hoyrup
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.
{"title":"Descriptive complexity of topological invariants","authors":"Djamel Eddine Amir, 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":"2025-05-14","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}
Pub Date : 2025-05-12DOI: 10.1016/j.apal.2025.103612
Wesley Calvert , Douglas Cenzer , David Gonzalez , Valentina Harizanov
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the hierarchy. We focus on linear orderings. We show that at the level, all linear orderings have both generically and coarsely computable copies. This behavior changes abruptly at higher levels; we show that at the level for any the set of linear orderings with generically or coarsely computable copies is -complete and therefore maximally complicated. This development is new even in the general analysis of generic and coarse computability of countable structures. In the process of proving these results, we introduce new tools for understanding generically and coarsely computable structures. We are able to give a purely structural statement that is equivalent to having a generically computable copy and show that every relational structure with only finitely many relations has coarsely and generically computable copies at the lowest level of the hierarchy.
{"title":"Generically computable linear orderings","authors":"Wesley Calvert , Douglas Cenzer , David Gonzalez , Valentina Harizanov","doi":"10.1016/j.apal.2025.103612","DOIUrl":"10.1016/j.apal.2025.103612","url":null,"abstract":"<div><div>We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mi>β</mi></mrow></msub></math></span> hierarchy. We focus on linear orderings. We show that at the <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> level, all linear orderings have both generically and coarsely computable copies. This behavior changes abruptly at higher levels; we show that at the <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mi>α</mi><mo>+</mo><mn>2</mn></mrow></msub></math></span> level for any <span><math><mi>α</mi><mo>∈</mo><msubsup><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>C</mi><mi>K</mi></mrow></msubsup></math></span> the set of linear orderings with generically or coarsely computable copies is <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>-complete and therefore maximally complicated. This development is new even in the general analysis of generic and coarse computability of countable structures. In the process of proving these results, we introduce new tools for understanding generically and coarsely computable structures. We are able to give a purely structural statement that is equivalent to having a generically computable copy and show that every relational structure with only finitely many relations has coarsely and generically computable copies at the lowest level of the hierarchy.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 8","pages":"Article 103612"},"PeriodicalIF":0.6,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943554","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}
Pub Date : 2025-05-08DOI: 10.1016/j.apal.2025.103609
Rafał Filipów, Adam Kwela
We examine topological spaces not distinguishing ideal pointwise and ideal σ-uniform convergence of sequences of real-valued continuous functions defined on them. For instance, we introduce a purely combinatorial cardinal characteristic (a sort of the bounding number ) and prove that it describes the minimal cardinality of topological spaces which distinguish ideal pointwise and ideal σ-uniform convergence. Moreover, we provide examples of topological spaces (focusing on subsets of reals) that do or do not distinguish the considered convergences. Since similar investigations for ideal quasi-normal convergence instead of ideal σ-uniform convergence have been performed in literature, we also study spaces not distinguishing ideal quasi-normal and ideal σ-uniform convergence of sequences of real-valued continuous functions defined on them.
{"title":"Spaces not distinguishing ideal pointwise and σ-uniform convergence","authors":"Rafał Filipów, Adam Kwela","doi":"10.1016/j.apal.2025.103609","DOIUrl":"10.1016/j.apal.2025.103609","url":null,"abstract":"<div><div>We examine topological spaces not distinguishing ideal pointwise and ideal <em>σ</em>-uniform convergence of sequences of real-valued continuous functions defined on them. For instance, we introduce a purely combinatorial cardinal characteristic (a sort of the bounding number <span><math><mi>b</mi></math></span>) and prove that it describes the minimal cardinality of topological spaces which distinguish ideal pointwise and ideal <em>σ</em>-uniform convergence. Moreover, we provide examples of topological spaces (focusing on subsets of reals) that do or do not distinguish the considered convergences. Since similar investigations for ideal quasi-normal convergence instead of ideal <em>σ</em>-uniform convergence have been performed in literature, we also study spaces not distinguishing ideal quasi-normal and ideal <em>σ</em>-uniform convergence of sequences of real-valued continuous functions defined on them.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103609"},"PeriodicalIF":0.6,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943439","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}
Pub Date : 2025-05-08DOI: 10.1016/j.apal.2025.103610
Tomasz Kowalski , Katarzyna Słomczyńska
We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra terms, simpler proofs of several existing results. As a by-product, we obtain an isomorphism between the free pseudocomplemented semilattice and the poset of join-irreducibles of the free p-algebra augmented by zero.
{"title":"Free p-algebras revisited: An algebraic investigation of implication-free intuitionism","authors":"Tomasz Kowalski , Katarzyna Słomczyńska","doi":"10.1016/j.apal.2025.103610","DOIUrl":"10.1016/j.apal.2025.103610","url":null,"abstract":"<div><div>We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra terms, simpler proofs of several existing results. As a by-product, we obtain an isomorphism between the free pseudocomplemented semilattice and the poset of join-irreducibles of the free p-algebra augmented by zero.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 9","pages":"Article 103610"},"PeriodicalIF":0.6,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943440","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：