Mathematical Logic Quarterly最新文献

{"title":"On Structures of Sign-Boundary and Diagonal Vacancy-Type Standard Contradictions","authors":"Xingxing He,&nbsp;Lan Pan,&nbsp;Yingfang Li,&nbsp;Jun Liu,&nbsp;Luis Martínez","doi":"10.1002/malq.70010","DOIUrl":"https://doi.org/10.1002/malq.70010","url":null,"abstract":"<div>\u0000 \u0000 <p>Automated deduction based on contradiction separation extends the binary resolution principle, offering a novel approach to deductive inference rules. Constructing standard contradictions is essential for its efficiency. This paper systematically investigates two new types of standard contradictions in propositional and first-order logic, enriching the library of standard contradictions and enhancing its effectiveness. First, we define two types of standard contradictions: sign-boundary contradictions and diagonal vacancy-type contradictions. Next, we propose the corresponding construction methods and present their properties related to contradiction composition and literal addition. Furthermore, we explore the transformations between these two types of contradictions and analyze the conditions necessary to construct standard contradictions. Finally, we extend these findings to first-order logic, demonstrating their applicability in more complex logical systems.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Triangular Norms on Partially Ordered Sets","authors":"Yong Su,&nbsp;Feng Tian,&nbsp;Wenwen Zong,&nbsp;Radko Mesiar","doi":"10.1002/malq.70014","DOIUrl":"https://doi.org/10.1002/malq.70014","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we extend the additively generated triangular norms from the framework of the unit interval to that of partially ordered sets. We present several conditions under which this formula <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ψ</mi>\u0000 <mi>T</mi>\u0000 <mo>(</mo>\u0000 <mi>φ</mi>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>φ</mi>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$psi T(varphi x, varphi y)$</annotation>\u0000 </semantics></math> yields a t-norm, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mo>,</mo>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 <annotation>$P, Q$</annotation>\u0000 </semantics></math> are partially ordered sets, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>φ</mi>\u0000 <mo>:</mo>\u0000 <mi>P</mi>\u0000 <mo>→</mo>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 <annotation>$varphi: P rightarrow Q$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ψ</mi>\u0000 <mo>:</mo>\u0000 <mi>Q</mi>\u0000 <mo>→</mo>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <annotation>$psi: Q rightarrow P$</annotation>\u0000 </semantics></math> are monotone functions and <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> is a t-norm/t-conorm on <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$Q$</annotation>\u0000 </semantics></math>. The partially ordered semigroups induced by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ψ</mi>\u0000 <mi>T</mi>\u0000 <mo>(</mo>\u0000 <mi>φ</mi>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>φ</mi>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$psi T(varphi x, varphi y)$</annotation>\u0000 </semantics></math> are order-preserving/order-reversing homomorphic to semigroup deformations of the semigroup induced by <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147564600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ideal Analytic Sets","authors":"Łukasz Mazurkiewicz,&nbsp;Szymon Żeberski","doi":"10.1002/malq.70012","DOIUrl":"10.1002/malq.70012","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this study is to give natural examples of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Σ</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Sigma }_1^1}$</annotation>\u0000 </semantics></math>-complete and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Π</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Pi }_1^1}$</annotation>\u0000 </semantics></math>-complete sets.</p>\u0000 <p>In the first part, we consider ideals on <span></span><math>\u0000 <semantics>\u0000 <mi>ω</mi>\u0000 <annotation>$omega$</annotation>\u0000 </semantics></math>. We use a unified approach introduced in [4] to create reductions of the collection of ill-founded trees to the ideals, proving <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Σ</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Sigma }_1^1}$</annotation>\u0000 </semantics></math>-completeness of the ideals.</p>\u0000 <p>In the second part, we show the connection between this topic, families of trees and coding of <span></span><math>\u0000 <semantics>\u0000 <mi>σ</mi>\u0000 <annotation>$sigma$</annotation>\u0000 </semantics></math>-ideals of Polish spaces. In particular, we use the unified approach to prove that sets of codes for closed Ramsey-null sets, for closed <span></span><math>\u0000 <semantics>\u0000 <mi>σ</mi>\u0000 <annotation>$sigma$</annotation>\u0000 </semantics></math>-compact sets and for closed not strongly dominating sets are <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Π</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Pi }_1^1}$</annotation>\u0000 </semantics></math>-complete.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ideal Analytic Sets","authors":"Łukasz Mazurkiewicz,&nbsp;Szymon Żeberski","doi":"10.1002/malq.70012","DOIUrl":"10.1002/malq.70012","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this study is to give natural examples of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Σ</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Sigma }_1^1}$</annotation>\u0000 </semantics></math>-complete and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Π</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Pi }_1^1}$</annotation>\u0000 </semantics></math>-complete sets.</p>\u0000 <p>In the first part, we consider ideals on <span></span><math>\u0000 <semantics>\u0000 <mi>ω</mi>\u0000 <annotation>$omega$</annotation>\u0000 </semantics></math>. We use a unified approach introduced in [4] to create reductions of the collection of ill-founded trees to the ideals, proving <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Σ</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Sigma }_1^1}$</annotation>\u0000 </semantics></math>-completeness of the ideals.</p>\u0000 <p>In the second part, we show the connection between this topic, families of trees and coding of <span></span><math>\u0000 <semantics>\u0000 <mi>σ</mi>\u0000 <annotation>$sigma$</annotation>\u0000 </semantics></math>-ideals of Polish spaces. In particular, we use the unified approach to prove that sets of codes for closed Ramsey-null sets, for closed <span></span><math>\u0000 <semantics>\u0000 <mi>σ</mi>\u0000 <annotation>$sigma$</annotation>\u0000 </semantics></math>-compact sets and for closed not strongly dominating sets are <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Π</mi>\u0000 <mn>1</mn>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$operatorname{mathbf {Pi }_1^1}$</annotation>\u0000 </semantics></math>-complete.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convex Structures and Homomorphisms in Ordered Fuzzy Rings: An Algebraic Perspective","authors":"Faisal Mehmood,&nbsp;Fu-Gui Shi,&nbsp;Tahir Mahmood,&nbsp;Muhammad Sajjad,&nbsp;Heng Liu","doi":"10.1002/malq.70009","DOIUrl":"https://doi.org/10.1002/malq.70009","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This study introduces a novel fuzzy algebraic structure, termed “convex ordered fuzzy subrings” (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;COFSR&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {COFSR}s$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), within the framework of “ordered fuzzy rings” (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;OFR&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {OFR}s$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;). We provide a rigorous formalization of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-subrings, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-ideals, and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convex substructures, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denotes a complete lattice equipped with a binary, order-compatible t-norm, integrating concepts from convexity theory, fuzzy set theory, and Heyting algebra. We investigate the preservation of convexity and order under ordered fuzzy ring homomorphisms (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;OFRH&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {OFRH}s$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) and their kernels, focusing on convex &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-subrings that are closed under fuzzy addition, multiplication, and additive inverses. These substructures induce &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convex structures with closure properties under Cartesian products and infima, and their behavior under homomorphisms highlights their algebraic and topological significance. Using an axiomatic framework, we establish conditions on lattice-valued binary operations necessary to maintain convexity in fuzzy substructures. Illustrative examples, structural analyses, and interconnections are provided to substantiate these results. This work addresses existing theoretical gaps in fuzzification, ordering, convexity, and homomorphic mappings, offering a unified foundation for the study of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convex Structures and Homomorphisms in Ordered Fuzzy Rings: An Algebraic Perspective","authors":"Faisal Mehmood,&nbsp;Fu-Gui Shi,&nbsp;Tahir Mahmood,&nbsp;Muhammad Sajjad,&nbsp;Heng Liu","doi":"10.1002/malq.70009","DOIUrl":"10.1002/malq.70009","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This study introduces a novel fuzzy algebraic structure, termed “convex ordered fuzzy subrings” (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;COFSR&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {COFSR}s$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), within the framework of “ordered fuzzy rings” (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;OFR&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {OFR}s$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;). We provide a rigorous formalization of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-subrings, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-ideals, and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convex substructures, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denotes a complete lattice equipped with a binary, order-compatible t-norm, integrating concepts from convexity theory, fuzzy set theory, and Heyting algebra. We investigate the preservation of convexity and order under ordered fuzzy ring homomorphisms (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;OFRH&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {OFRH}s$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) and their kernels, focusing on convex &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-subrings that are closed under fuzzy addition, multiplication, and additive inverses. These substructures induce &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {L}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convex structures with closure properties under Cartesian products and infima, and their behavior under homomorphisms highlights their algebraic and topological significance. Using an axiomatic framework, we establish conditions on lattice-valued binary operations necessary to maintain convexity in fuzzy substructures. Illustrative examples, structural analyses, and interconnections are provided to substantiate these results. This work addresses existing theoretical gaps in fuzzification, ordering, convexity, and homomorphic mappings, offering a unified foundation for the study of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniform Local Weak o-Minimality and \u0000 \u0000 ∗\u0000 $*$\u0000 -Local Weak o-Minimality","authors":"Masato Fujita","doi":"10.1002/malq.70002","DOIUrl":"https://doi.org/10.1002/malq.70002","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose the notions of uniform local weak o-minimality and <span></span><math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-local weak o-minimality. Local monotonicity theorems hold in definably complete locally o-minimal structures and uniformly locally o-minimal structures of the second kind. In this paper, we demonstrate new local monotonicity theorems for uniformly locally weakly o-minimal structures of the second kind and for locally o-minimal structures under the assumption called the univariate <span></span><math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-continuity property. We also prove that several formulas for dimension of definable sets, which hold in definably complete locally o-minimal structures, also hold in <span></span><math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-locally weakly o-minimal structures possessing the univariate <span></span><math>\u0000 <semantics>\u0000 <mo>∗</mo>\u0000 <annotation>$*$</annotation>\u0000 </semantics></math>-continuity property.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"71 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145626691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Decidable quasivarieties of p-algebras","authors":"Tomasz Kowalski,&nbsp;Katarzyna Słomczyńska","doi":"10.1002/malq.202300064","DOIUrl":"https://doi.org/10.1002/malq.202300064","url":null,"abstract":"<p>We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.</p>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"71 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Limit models in strictly stable abstract elementary classes","authors":"Will Boney,&nbsp;Monica M. VanDieren","doi":"10.1002/malq.202200075","DOIUrl":"https://doi.org/10.1002/malq.202200075","url":null,"abstract":"<p>In this paper, we examine the locality condition for non-splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove the following. Suppose that <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$mathcal {K}$</annotation>\u0000 </semantics></math> is an abstract elementary class satisfying\u0000\u0000 </p><p>Then for <span></span><math>\u0000 <semantics>\u0000 <mi>ϑ</mi>\u0000 <annotation>$vartheta$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>δ</mi>\u0000 <annotation>$delta$</annotation>\u0000 </semantics></math> limit ordinals <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>&lt;</mo>\u0000 <msup>\u0000 <mi>μ</mi>\u0000 <mo>+</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$&lt;mu ^+$</annotation>\u0000 </semantics></math> both with cofinality <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>≥</mo>\u0000 <msubsup>\u0000 <mi>κ</mi>\u0000 <mi>μ</mi>\u0000 <mo>∗</mo>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$ge kappa ^*_mu (mathcal {K})$</annotation>\u0000 </semantics></math>, if <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$mathcal {K}$</annotation>\u0000 </semantics></math> satisfies symmetry for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>non</mi>\u0000 <mi>-</mi>\u0000 <mi>μ</mi>\u0000 <mi>-</mi>\u0000 <mi>splitting</mi>\u0000 </mrow>\u0000 <annotation>${rm non}text{-}mutext{-}{rm splitting}$</annotation>\u0000 </semantics></math> (or just <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>μ</mi>\u0000 <mo>,</mo>\u0000 <mi>δ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(mu,delta)$</annotation>\u0000 </semantics></math>-symmetry), then, for any <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$M_1$</annotation>\u0000 </semantics></math> ","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"70 4","pages":"438-453"},"PeriodicalIF":0.4,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/malq.202200075","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Random graph coloring and the instability","authors":"Akito Tsuboi","doi":"10.1002/malq.202300043","DOIUrl":"https://doi.org/10.1002/malq.202300043","url":null,"abstract":"<p>This paper explores the coloring problem, focusing on the existence of uniformly colored substructures. The study primarily examines random graphs with edge coloring and their generic substructures. The key finding is that the absence of a monochromatic generic substructure corresponds to increased instability, meaning that the colored random graph hereditarily possesses the strict order property.</p>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"70 4","pages":"429-437"},"PeriodicalIF":0.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}