发布求助
文献互助 智能选刊 最新文献

Archive for Mathematical Logic最新文献

筛选
英文 中文
Questions on cardinal invariants of Boolean algebras 布尔代数的基数不变量问题
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-05-18 DOI: 10.1007/s00153-023-00872-8
Mario Jardón Santos
{"title":"Questions on cardinal invariants of Boolean algebras","authors":"Mario Jardón Santos","doi":"10.1007/s00153-023-00872-8","DOIUrl":"10.1007/s00153-023-00872-8","url":null,"abstract":"<div><p>In the book Cardinal Invariants on Boolean Algebras by J. Donald Monk many such cardinal functions are defined and studied. Among them several are generalizations of well known cardinal characteristics of the continuum. Alongside a long list of open problems is given. Focusing on half a dozen of those cardinal invariants some of those problems are given an answer here, which in most of the cases is a definitive one. Most of them can be divided in two groups. The problems of the first group ask about the change on those cardinal functions when going from a given infinite Boolean algebra to its simple extensions, while in the second group the comparison is between a couple of given infinite Boolean algebras and their free product.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"947 - 963"},"PeriodicalIF":0.3,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00872-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44557674","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: 2
Mathias and silver forcing parametrized by density Mathias和silver力的密度参数化
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-05-18 DOI: 10.1007/s00153-023-00881-7
Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle
{"title":"Mathias and silver forcing parametrized by density","authors":"Giorgio Laguzzi,&nbsp;Heike Mildenberger,&nbsp;Brendan Stuber-Rousselle","doi":"10.1007/s00153-023-00881-7","DOIUrl":"10.1007/s00153-023-00881-7","url":null,"abstract":"<div><p>We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse <span>(2^omega )</span> to <span>(omega )</span>, while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"965 - 990"},"PeriodicalIF":0.3,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00881-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44594215","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: 1
Definable Tietze extension property in o-minimal expansions of ordered groups 有序群o-极小展开中可定义的Tietze扩张性质
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-05-15 DOI: 10.1007/s00153-023-00875-5
Masato Fujita
{"title":"Definable Tietze extension property in o-minimal expansions of ordered groups","authors":"Masato Fujita","doi":"10.1007/s00153-023-00875-5","DOIUrl":"10.1007/s00153-023-00875-5","url":null,"abstract":"<div><p>The following two assertions are equivalent for an o-minimal expansion of an ordered group <span>(mathcal M=(M,&lt;,+,0,ldots ))</span>. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function <span>(f:A rightarrow M)</span> defined on a definable closed subset of <span>(M^n)</span> has a definable continuous extension <span>(F:M^n rightarrow M)</span>.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"941 - 945"},"PeriodicalIF":0.3,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44364332","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
Correction to: Towers, mad families, and unboundedness 更正:塔，疯狂的家庭，和无边界
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-04-03 DOI: 10.1007/s00153-023-00870-w
Vera Fischer, Marlene Koelbing, Wolfgang Wohofsky
{"title":"Correction to: Towers, mad families, and unboundedness","authors":"Vera Fischer, Marlene Koelbing, Wolfgang Wohofsky","doi":"10.1007/s00153-023-00870-w","DOIUrl":"https://doi.org/10.1007/s00153-023-00870-w","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 1","pages":"1159-1160"},"PeriodicalIF":0.3,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52099430","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
Correction to: Towers, mad families, and unboundedness 更正:塔，疯狂的家庭，和无边界
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-04-03 DOI: 10.1007/s00153-023-00870-w
Vera Fischer, Marlene Koelbing, Wolfgang Wohofsky
{"title":"Correction to: Towers, mad families, and unboundedness","authors":"Vera Fischer,&nbsp;Marlene Koelbing,&nbsp;Wolfgang Wohofsky","doi":"10.1007/s00153-023-00870-w","DOIUrl":"10.1007/s00153-023-00870-w","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"1159 - 1160"},"PeriodicalIF":0.3,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00870-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50005182","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
Consistency and interpolation in linear continuous logic 线性连续逻辑中的一致性与插值
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-03-21 DOI: 10.1007/s00153-023-00869-3
Mahya Malekghasemi, Seyed-Mohammad Bagheri
{"title":"Consistency and interpolation in linear continuous logic","authors":"Mahya Malekghasemi,&nbsp;Seyed-Mohammad Bagheri","doi":"10.1007/s00153-023-00869-3","DOIUrl":"10.1007/s00153-023-00869-3","url":null,"abstract":"<div><p>We prove Robinson consistency theorem as well as Craig, Lyndon and Herbrand interpolation theorems in linear continuous logic.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"931 - 939"},"PeriodicalIF":0.3,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43271849","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
The axiom of choice in metric measure spaces and maximal (delta )-separated sets 度量度量空间和极大(delta )分离集中的选择公理
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-03-13 DOI: 10.1007/s00153-023-00868-4
Michał Dybowski, Przemysław Górka
{"title":"The axiom of choice in metric measure spaces and maximal (delta )-separated sets","authors":"Michał Dybowski,&nbsp;Przemysław Górka","doi":"10.1007/s00153-023-00868-4","DOIUrl":"10.1007/s00153-023-00868-4","url":null,"abstract":"<div><p>We show that the Axiom of Countable Choice is necessary and sufficient to prove that the existence of a Borel measure on a pseudometric space such that the measure of open balls is positive and finite implies separability of the space. In this way a negative answer to an open problem formulated in Górka (Am Math Mon 128:84–86, 2020) is given. Moreover, we study existence of maximal <span>(delta )</span>-separated sets in metric and pseudometric spaces from the point of view the Axiom of Choice and its weaker forms.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 5-6","pages":"735 - 749"},"PeriodicalIF":0.3,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00868-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50048305","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
A topological completeness theorem for transfinite provability logic 超限可证明性逻辑的拓扑完备性定理
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-02-22 DOI: 10.1007/s00153-023-00863-9
Juan P. Aguilera
{"title":"A topological completeness theorem for transfinite provability logic","authors":"Juan P. Aguilera","doi":"10.1007/s00153-023-00863-9","DOIUrl":"10.1007/s00153-023-00863-9","url":null,"abstract":"<div><p>We prove a topological completeness theorem for the modal logic <span>(textsf{GLP})</span> containing operators <span>({langle xi rangle :xi in textsf{Ord}})</span> intended to capture a wellordered sequence of consistency operators increasing in strength. More specifically, we prove that, given a tall-enough scattered space <i>X</i>, any sentence <span>(phi )</span> consistent with <span>(textsf{GLP})</span> can be satisfied on a polytopological space based on finitely many Icard topologies constructed over <i>X</i> and corresponding to the finitely many modalities that occur in <span>(phi )</span>.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 5-6","pages":"751 - 788"},"PeriodicalIF":0.3,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00863-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50042104","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: 1
Sets of real numbers closed under Turing equivalence: applications to fields, orders and automorphisms 在图灵等价下闭合的实数集：域、阶和自同构的应用
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-02-16 DOI: 10.1007/s00153-023-00865-7
Iván Ongay-Valverde
{"title":"Sets of real numbers closed under Turing equivalence: applications to fields, orders and automorphisms","authors":"Iván Ongay-Valverde","doi":"10.1007/s00153-023-00865-7","DOIUrl":"10.1007/s00153-023-00865-7","url":null,"abstract":"<div><p>In the first half of this paper, we study the way that sets of real numbers closed under Turing equivalence sit inside the real line from the perspective of algebra, measure and orders. Afterwards, we combine the results from our study of these sets as orders with a classical construction from Avraham to obtain a restriction about how non trivial automorphism of the Turing degrees (if they exist) interact with 1-generic degrees.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 5-6","pages":"843 - 869"},"PeriodicalIF":0.3,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44115779","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
Ideals with Smital properties 具有Smital属性的理想
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-02-14 DOI: 10.1007/s00153-023-00867-5
Marcin Michalski, Robert Rałowski, Szymon Żeberski
{"title":"Ideals with Smital properties","authors":"Marcin Michalski,&nbsp;Robert Rałowski,&nbsp;Szymon Żeberski","doi":"10.1007/s00153-023-00867-5","DOIUrl":"10.1007/s00153-023-00867-5","url":null,"abstract":"<div><p>A <span>(sigma )</span>-ideal <span>(mathcal {I})</span> on a Polish group <span>((X,+))</span> has the Smital Property if for every dense set <i>D</i> and a Borel <span>(mathcal {I})</span>-positive set <i>B</i> the algebraic sum <span>(D+B)</span> is a complement of a set from <span>(mathcal {I})</span>. We consider several variants of this property and study their connections with the countable chain condition, maximality and how well they are preserved via Fubini products. In particular we show that there are <span>(mathfrak {c})</span> many maximal invariant <span>(sigma )</span>-ideals with Borel bases on the Cantor space <span>(2^omega )</span>.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 5-6","pages":"831 - 842"},"PeriodicalIF":0.3,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00867-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45603623","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信