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Another method to add a closed unbounded set of former regulars 另一种添加前正则的封闭无界集合的方法
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2026-03-19 DOI: 10.1007/s00153-026-01008-4
Moti Gitik, Sittinon Jirattikansakul
{"title":"Another method to add a closed unbounded set of former regulars","authors":"Moti Gitik,&nbsp;Sittinon Jirattikansakul","doi":"10.1007/s00153-026-01008-4","DOIUrl":"10.1007/s00153-026-01008-4","url":null,"abstract":"<div><p>A club consisting of former regulars is added to an inaccessible cardinal, without changing cofinalities outside it. The initial assumption is optimal. A variation of the Radin forcing without a top measurable cardinal is introduced for this.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 4","pages":"509 - 529"},"PeriodicalIF":0.4,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147707807","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}
引用次数: 0
Dominating numbers at singular cardinals 在单数基数上占主导地位
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2026-03-19 DOI: 10.1007/s00153-026-01009-3
Yusuke Hayashi
{"title":"Dominating numbers at singular cardinals","authors":"Yusuke Hayashi","doi":"10.1007/s00153-026-01009-3","DOIUrl":"10.1007/s00153-026-01009-3","url":null,"abstract":"<div><p>We study the generalized dominating number <span>(mathfrak {d}_{mu })</span> at a singular cardinal <span>(mu )</span> of cofinality <span>(kappa )</span>. We prove two basic lower bounds: in <span>(text {ZFC})</span>, <span>(text {cf}left( {[mu ]^kappa ,subseteq }right) le mathfrak {d}_{mu })</span>, and under mild cardinal-arithmetic assumptions, <span>(2^{&lt;mu } le mathfrak {d}_{mu })</span>. We also clarify when <span>(mathfrak {d}_{mu })</span> can differ from <span>(2^mu )</span>: assuming <span>(text {GCH})</span> and <span>(kappa = text {cf}left( {mu }right) &gt; omega )</span>, a finite-support iteration of Cohen forcing of length <span>(mu ^{++})</span> yields <span>(mathfrak {d}_{mu }&lt; 2^mu )</span>. On the other hand, for <span>(kappa = text {cf}left( {mu }right) = omega )</span>, natural <span>(mu )</span>-cc posets force <span>(mathfrak {d}_{mu }= 2^mu .)</span></p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 4","pages":"531 - 544"},"PeriodicalIF":0.4,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147707804","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}
引用次数: 0
Monotonicity of the ultrafilter number function 超滤数函数的单调性
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2026-03-12 DOI: 10.1007/s00153-026-01010-w
Toshimichi Usuba
{"title":"Monotonicity of the ultrafilter number function","authors":"Toshimichi Usuba","doi":"10.1007/s00153-026-01010-w","DOIUrl":"10.1007/s00153-026-01010-w","url":null,"abstract":"<div><p>We investigate whether the ultrafilter number function <span>(kappa mapsto mathfrak {u}(kappa ))</span> on the cardinals is monotone, that is, whether <span>(mathfrak {u}(lambda ) le mathfrak {u}(kappa ))</span> holds for all cardinals <span>(lambda &lt; kappa )</span> or not. We show that monotonicity can fail, but the failure has large cardinal strength. On the other hand, we prove that there are many restrictions of the failure of monotonicity. For instance, if <span>(kappa )</span> is a singular cardinal with countable cofinality or a strong limit singular cardinal, then <span>(mathfrak {u}(kappa ) le mathfrak {u}(kappa ^+))</span> holds.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 4","pages":"545 - 568"},"PeriodicalIF":0.4,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-026-01010-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147707805","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}
引用次数: 0
The adjacent Hindman’s Theorem and the (mathbb Z)-Ramsey’s Theorem 相邻的欣德曼定理和(mathbb Z) -拉姆齐定理
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2026-03-10 DOI: 10.1007/s00153-026-01004-8
Bruno Fernando Aceves-Martínez, David J. Fernández-Bretón, L. F. Romero-García, Luis F. Villagómez-Canela
{"title":"The adjacent Hindman’s Theorem and the (mathbb Z)-Ramsey’s Theorem","authors":"Bruno Fernando Aceves-Martínez,&nbsp;David J. Fernández-Bretón,&nbsp;L. F. Romero-García,&nbsp;Luis F. Villagómez-Canela","doi":"10.1007/s00153-026-01004-8","DOIUrl":"10.1007/s00153-026-01004-8","url":null,"abstract":"<div><p>We consider the restriction of Ramsey’s theorem that arises from considering only translation-invariant colourings of pairs, and show that this has the same strength (both from the viewpoint of Reverse Mathematics and from the viewpoint of Computability Theory) as the <i>Adjacent Hindman’s Theorem</i>, proposed by L. Carlucci (Arch. Math. Log. <b>57</b> (2018), 381–359). We also investigate some higher dimensional versions of both of these statements.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 4","pages":"451 - 463"},"PeriodicalIF":0.4,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147707806","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}
引用次数: 0
Small measurable cardinals 小的可测量基数
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2026-02-28 DOI: 10.1007/s00153-026-01006-6
Yair Hayut, Asaf Karagila
{"title":"Small measurable cardinals","authors":"Yair Hayut,&nbsp;Asaf Karagila","doi":"10.1007/s00153-026-01006-6","DOIUrl":"10.1007/s00153-026-01006-6","url":null,"abstract":"<div><p>We continue the work from [8] and make a small—but significant—improvement to the definition of <i>j</i>-decomposable system. This provides us with a better lifting of elementary embeddings to symmetric extensions. In particular, this allows us to more easily lift weakly compact embeddings and thus preserve the notion of weakly critical cardinals. We use this improved lifting criterion to show that the first measurable cardinal can be the first weakly critical cardinal or the first Mahlo cardinal, both relative to the existence of a single measurable cardinal. However, if the first inaccessible cardinal is the first measurable cardinal, then in a suitable inner model it has Mitchell order of at least 2.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 4","pages":"465 - 475"},"PeriodicalIF":0.4,"publicationDate":"2026-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-026-01006-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147707802","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}
引用次数: 0
Borel complexity of families of finite equivalence relations via large cardinals 通过大基数的有限等价关系族的Borel复杂度
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2026-02-26 DOI: 10.1007/s00153-026-01007-5
Michael C. Laskowski, Danielle S. Ulrich
{"title":"Borel complexity of families of finite equivalence relations via large cardinals","authors":"Michael C. Laskowski,&nbsp;Danielle S. Ulrich","doi":"10.1007/s00153-026-01007-5","DOIUrl":"10.1007/s00153-026-01007-5","url":null,"abstract":"<div><p>We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an <span>(omega )</span>-Erdős cardinal, we determine which of these theories are Borel complete. We develop machinery, including <i>forbidding nested sequences</i> which implies a tight upper bound on Borel complexity, and <i>admitting cross-cutting absolutely indiscernible sets</i> which in our context implies Borel completeness.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 4","pages":"477 - 508"},"PeriodicalIF":0.4,"publicationDate":"2026-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-026-01007-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147707803","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}
引用次数: 0
Characterization of subdirectly irreducible heyting algebras with negative tense operators 具有负时态算子的次直接不可约heyting代数的性质
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2026-01-16 DOI: 10.1007/s00153-025-01001-3
Federico Almiñana, Gustavo Pelaitay
{"title":"Characterization of subdirectly irreducible heyting algebras with negative tense operators","authors":"Federico Almiñana,&nbsp;Gustavo Pelaitay","doi":"10.1007/s00153-025-01001-3","DOIUrl":"10.1007/s00153-025-01001-3","url":null,"abstract":"<div><p>In (Intuitionistic propositional logic with galois negations. Stud Logica 111:21–56, 2023) , Ma and Li established Intuitionistic Propositional Logic with Galois negations (IGN). These logics can be viewed as the ordered dualization of Ewald’s intuitionistic tense logic IKt, where Galois negations function as the ordered duals of residuated pairs of tense operators. In Almiñana et al. (On heyting algebras with negative tense operators. Stud Logica 111:1015–1036, 2023), we introduced the concept of negative tense operators on Heyting algebras and defined the variety of tense H-algebras. This new variety of algebras serves as the algebraic semantics for IGN. In this paper, we extend our investigation into tense H-algebras, focusing specifically on their topological properties. Particularly, we provide a topological characterization of subdirectly irreducible tense H-algebras.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 3","pages":"425 - 449"},"PeriodicalIF":0.4,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147618013","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}
引用次数: 0
Limits on forcing axioms at (omega _2) compatible with the continuum hypothesis 在(omega _2)与连续统假设相容的强迫公理的限制
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2025-12-17 DOI: 10.1007/s00153-025-01003-1
Stevo Todorcevic, Shihao Xiong
{"title":"Limits on forcing axioms at (omega _2) compatible with the continuum hypothesis","authors":"Stevo Todorcevic,&nbsp;Shihao Xiong","doi":"10.1007/s00153-025-01003-1","DOIUrl":"10.1007/s00153-025-01003-1","url":null,"abstract":"<div><p>We show that the forcing axiom for countably compact, <span>(omega _2)</span>-Knaster, well-met posets is inconsistent. This is supplemental to an inconsistency result of Shelah [9] and sets a new limit to the generalization of Martin’s Axiom to the stage of <span>(omega _2)</span>.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 3","pages":"411 - 423"},"PeriodicalIF":0.4,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147617978","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}
引用次数: 0
Logical complexity of reducts of elementary algebraic classes 初等代数类约简的逻辑复杂性
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2025-12-14 DOI: 10.1007/s00153-025-01002-2
Carles Cardó
{"title":"Logical complexity of reducts of elementary algebraic classes","authors":"Carles Cardó","doi":"10.1007/s00153-025-01002-2","DOIUrl":"10.1007/s00153-025-01002-2","url":null,"abstract":"<div><p>We examine how elementary classes of algebras can be represented as reducts of logically simpler classes. For example, we demonstrate that every elementary class is a reduct of a positive class, and that any variety is a reduct of a four-based variety. Additionally, we introduce hierarchies based on fragments of first-order logic to analyse these reducts, providing a more detailed structural understanding of the landscape of algebraic classes.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 3","pages":"391 - 409"},"PeriodicalIF":0.4,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147617977","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}
引用次数: 0
A general approach to asymptotic elimination of aggregation functions and generalized quantifiers 聚合函数和广义量词渐近消去的一般方法
IF 0.4 4区 数学
Archive for Mathematical Logic Pub Date : 2025-11-25 DOI: 10.1007/s00153-025-01000-4
Vera Koponen, Felix Weitkämper
{"title":"A general approach to asymptotic elimination of aggregation functions and generalized quantifiers","authors":"Vera Koponen,&nbsp;Felix Weitkämper","doi":"10.1007/s00153-025-01000-4","DOIUrl":"10.1007/s00153-025-01000-4","url":null,"abstract":"<div><p>We consider a logic with truth values in the unit interval and which uses aggregation functions instead of quantifiers, and we describe a general approach to asymptotic elimination of aggregation functions and, indirectly, of asymptotic elimination of Mostowski style generalized quantifiers, since such can be expressed by using aggregation functions. The notion of “local continuity” of an aggregation function, which we make precise in two (related) ways, plays a central role in this approach.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"65 3","pages":"363 - 390"},"PeriodicalIF":0.4,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-025-01000-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147618014","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}
引用次数: 0
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