Archive for Mathematical Logic最新文献_第7页

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, Eleftherios Tachtsis","doi":"10.1007/s00153-023-00871-9","DOIUrl":"10.1007/s00153-023-00871-9","url":null,"abstract":"<div>We provide a general criterion for Fraenkel–Mostowski models of ({textsf{ZFA}}) (i.e. Zermelo–Fraenkel set theory weakened to permit the existence of atoms) which implies “every linearly ordered set can be well ordered” (({textsf{LW}})), and look at six models for ({textsf{ZFA}}) which satisfy this criterion (and thus ({textsf{LW}}) is true in these models) and “every Dedekind finite set is finite” (({textsf{DF}}={textsf{F}})) 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 (({textsf{MC}}_{aleph _{0}}^{aleph _{0}})) 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 (({textsf{AC}}^{{textsf{WO}}}_{{textsf{fin}}})) 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 ({textsf{AC}}^{{textsf{WO}}}_{{textsf{fin}}}) which is unknown. Models 4 and 5 are variations of Model 3. In Model 4 ({textsf{AC}}_{textrm{fin}}^{{textsf{WO}}}) 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 (2{mathfrak {m}} = {mathfrak {m}}) for every infinite cardinal number ({mathfrak {m}}). 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.</div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"1131 - 1157"},"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

引用次数: 0

The fixed point and the Craig interpolation properties for sublogics of (textbf{IL}) $$textbf{IL}子逻辑的不动点和Craig插值性质$$

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-06-10 DOI: 10.1007/s00153-023-00882-6

Sohei Iwata, Taishi Kurahashi, Yuya Okawa

引用次数: 0

On the complexity of the theory of a computably presented metric structure 论可计算度量结构理论的复杂性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-06-09 DOI: 10.1007/s00153-023-00884-4

Caleb Camrud, Isaac Goldbring, Timothy H. McNicholl

引用次数: 2

Recursive Polish spaces 递归抛光空间

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-06-09 DOI: 10.1007/s00153-023-00883-5

Tyler Arant

引用次数: 0

Structure of semisimple rings in reverse and computable mathematics 半单环的结构在逆向和可计算数学中的应用

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-06-08 DOI: 10.1007/s00153-023-00885-3

Huishan Wu

引用次数: 0

A syntactic approach to Borel functions: some extensions of Louveau’s theorem 博雷尔函数的句法方法:卢沃定理的一些扩展

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-06-02 DOI: 10.1007/s00153-023-00880-8

Takayuki Kihara, Kenta Sasaki

引用次数: 0

On the non-existence of (kappa )-mad families 关于不存在(kappa )疯狂家庭

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-05-23 DOI: 10.1007/s00153-023-00874-6

Haim Horowitz, Saharon Shelah

引用次数: 0

An AEC framework for fields with commuting automorphisms 具有交换自同构域的AEC框架

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-05-20 DOI: 10.1007/s00153-023-00879-1

Tapani Hyttinen, Kaisa Kangas

{"title":"An AEC framework for fields with commuting automorphisms","authors":"Tapani Hyttinen, Kaisa Kangas","doi":"10.1007/s00153-023-00879-1","DOIUrl":"10.1007/s00153-023-00879-1","url":null,"abstract":"<div>In this paper, we introduce an AEC framework for studying fields with commuting automorphisms. Fields with commuting automorphisms are closely related to difference fields. Some authors define a difference ring (or field) as a ring (or field) together with several commuting endomorphisms, while others only study one endomorphism. Z. Chatzidakis and E. Hrushovski have studied in depth the model theory of ACFA, the model companion of difference fields with one automorphism. Our fields with commuting automorphisms generalize this setting. We have several automorphisms and they are required to commute. Hrushovski has proved that in the case of fields with two or more commuting automorphisms, the existentially closed models do not necessarily form a first order model class. In the present paper, we introduce FCA-classes, an AEC framework for studying the existentially closed models of the theory of fields with commuting automorphisms. We prove that an FCA-class has AP and JEP and thus a monster model, that Galois types coincide with existential types in existentially closed models, that the class is homogeneous, and that there is a version of type amalgamation theorem that allows to combine three types under certain conditions. Finally, we use these results to show that our monster model is a simple homogeneous structure in the sense of S. Buechler and O. Lessman (this is a non-elementary analogue for the classification theoretic notion of a simple first order theory).</div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"1001 - 1032"},"PeriodicalIF":0.3,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00879-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45633905","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

The small index property for countable superatomic boolean algebras 可数超原子布尔代数的小指标性质

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-05-19 DOI: 10.1007/s00153-023-00876-4

J. K. Truss

引用次数: 0