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Punctually presented structures II: comparing presentations 按时展示的结构 II：展示比较
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-08-08 DOI: 10.1007/s00153-024-00940-7
Marina Dorzhieva, Rodney Downey, Ellen Hammatt, Alexander G. Melnikov, K. Ng
{"title":"Punctually presented structures II: comparing presentations","authors":"Marina Dorzhieva, Rodney Downey, Ellen Hammatt, Alexander G. Melnikov, K. Ng","doi":"10.1007/s00153-024-00940-7","DOIUrl":"https://doi.org/10.1007/s00153-024-00940-7","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141928836","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 Tarski–Lindenbaum algebra of the class of strongly constructivizable models with $$omega $$-stable theories 具有 $$omega $$ 稳定理论的强可构造模型类的塔尔斯基-林登鲍姆代数
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-06-08 DOI: 10.1007/s00153-024-00927-4
M. Peretyat’kin
{"title":"The Tarski–Lindenbaum algebra of the class of strongly constructivizable models with $$omega $$-stable theories","authors":"M. Peretyat’kin","doi":"10.1007/s00153-024-00927-4","DOIUrl":"https://doi.org/10.1007/s00153-024-00927-4","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141368907","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
Separablilty of metric measure spaces and choice axioms 度量空间的分离性和选择公理
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-05-21 DOI: 10.1007/s00153-024-00931-8
Paul Howard
{"title":"Separablilty of metric measure spaces and choice axioms","authors":"Paul Howard","doi":"10.1007/s00153-024-00931-8","DOIUrl":"https://doi.org/10.1007/s00153-024-00931-8","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141117609","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
Fragments of IOpen IOpen 的片段
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-05-20 DOI: 10.1007/s00153-024-00929-2
Konstantin Kovalyov
{"title":"Fragments of IOpen","authors":"Konstantin Kovalyov","doi":"10.1007/s00153-024-00929-2","DOIUrl":"https://doi.org/10.1007/s00153-024-00929-2","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120436","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
Convergence of measures after adding a real. 增加一个实数后，测量结果趋于一致。
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-01-01 Epub Date: 2023-08-11 DOI: 10.1007/s00153-023-00888-0
Damian Sobota, Lyubomyr Zdomskyy
{"title":"Convergence of measures after adding a real.","authors":"Damian Sobota, Lyubomyr Zdomskyy","doi":"10.1007/s00153-023-00888-0","DOIUrl":"10.1007/s00153-023-00888-0","url":null,"abstract":"<p><p>We prove that if <math><mi>A</mi></math> is an infinite Boolean algebra in the ground model <i>V</i> and <math><mi>P</mi></math> is a notion of forcing adding any of the following reals: a Cohen real, an unsplit real, or a random real, then, in any <math><mi>P</mi></math>-generic extension <i>V</i>[<i>G</i>], <math><mi>A</mi></math> has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.</p>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10787011/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52099468","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
Semi-honest subrecursive degrees and the collection rule in arithmetic 半诚实子递归度与算术中的集合规则
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-08-12 DOI: 10.1007/s00153-023-00889-z
Andrés Cordón-Franco, F. F. Lara-Martín
{"title":"Semi-honest subrecursive degrees and the collection rule in arithmetic","authors":"Andrés Cordón-Franco, F. F. Lara-Martín","doi":"10.1007/s00153-023-00889-z","DOIUrl":"https://doi.org/10.1007/s00153-023-00889-z","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44525200","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 Mathias criterion for the Magidor iteration of Prikry forcings Prikry强迫Magidor迭代的一个Mathias准则
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-08-04 DOI: 10.1007/s00153-023-00887-1
Omer Ben-Neria
{"title":"A Mathias criterion for the Magidor iteration of Prikry forcings","authors":"Omer Ben-Neria","doi":"10.1007/s00153-023-00887-1","DOIUrl":"https://doi.org/10.1007/s00153-023-00887-1","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41471612","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: 1
Herbrand complexity and the epsilon calculus with equality Herbrand复杂度和相等的微积分
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-07-29 DOI: 10.1007/s00153-023-00877-3
Kenji Miyamoto, G. Moser
{"title":"Herbrand complexity and the epsilon calculus with equality","authors":"Kenji Miyamoto, G. Moser","doi":"10.1007/s00153-023-00877-3","DOIUrl":"https://doi.org/10.1007/s00153-023-00877-3","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44538500","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
Models of ({{textsf{ZFA}}}) in which every linearly ordered set can be well ordered ({{textsf{ZFA}}})的模型，其中每个线性有序集都可以是有序的
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-06-13 DOI: 10.1007/s00153-023-00871-9
Paul Howard, Eleftherios Tachtsis
{"title":"Models of ({{textsf{ZFA}}}) in which every linearly ordered set can be well ordered","authors":"Paul Howard,&nbsp;Eleftherios Tachtsis","doi":"10.1007/s00153-023-00871-9","DOIUrl":"10.1007/s00153-023-00871-9","url":null,"abstract":"<div><p>We provide a general criterion for Fraenkel–Mostowski models of <span>({textsf{ZFA}})</span> (i.e. Zermelo–Fraenkel set theory weakened to permit the existence of atoms) which implies “every linearly ordered set can be well ordered” (<span>({textsf{LW}})</span>), and look at six models for <span>({textsf{ZFA}})</span> which satisfy this criterion (and thus <span>({textsf{LW}})</span> is true in these models) and “every Dedekind finite set is finite” (<span>({textsf{DF}}={textsf{F}})</span>) is true, and also consider various forms of choice for well-ordered families of well orderable sets in these models. In Model 1, the axiom of multiple choice for countably infinite families of countably infinite sets (<span>({textsf{MC}}_{aleph _{0}}^{aleph _{0}})</span>) is false. It was the open question of whether or not such a model exists (from Howard and Tachtsis “On metrizability and compactness of certain products without the Axiom of Choice”) that provided the motivation for this paper. In Model 2, which is constructed by first choosing an uncountable regular cardinal in the ground model, a strong form of Dependent choice is true, while the axiom of choice for well-ordered families of finite sets (<span>({textsf{AC}}^{{textsf{WO}}}_{{textsf{fin}}})</span>) is false. Also in this model the axiom of multiple choice for well-ordered families of well orderable sets fails. Model 3 is similar to Model 2 except for the status of <span>({textsf{AC}}^{{textsf{WO}}}_{{textsf{fin}}})</span> which is unknown. Models 4 and 5 are variations of Model 3. In Model 4 <span>({textsf{AC}}_{textrm{fin}}^{{textsf{WO}}})</span> is true. The construction of Model 5 begins by choosing a regular successor cardinal in the ground model. Model 6 is the only one in which <span>(2{mathfrak {m}} = {mathfrak {m}})</span> for every infinite cardinal number <span>({mathfrak {m}})</span>. We show that the union of a well-ordered family of well orderable sets is well orderable in Model 6 and that the axiom of multiple countable choice is false.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50023467","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
Models of ZFAdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${{textsf{ZFA}}}$$end{document} in which every linearly ZFAdocumentclass[12pt]｛minimum｝usepackage｛amsmath｝usepackage｛wasysym｝usepackup｛amsfonts｝usecpackage{amssymb｝usecpackage{amsbsy｝usecPackage｛mathrsfs｝usepackage{upgeek｝setlength｛oddsedmargin｝｛-69pt｝ begin｛document｝$$｛textsf｛ZFA｝｝｝$｝
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2023-06-13 DOI: 10.1007/s00153-023-00871-9
Paul Howard, E. Tachtsis
{"title":"Models of ZFAdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${{textsf{ZFA}}}$$end{document} in which every linearly ","authors":"Paul Howard, E. Tachtsis","doi":"10.1007/s00153-023-00871-9","DOIUrl":"https://doi.org/10.1007/s00153-023-00871-9","url":null,"abstract":"","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42828924","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
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