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
On computable numberings of families of Turing degrees 论图灵度族的可计算编号
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-03-18 DOI: 10.1007/s00153-024-00914-9
Marat Faizrahmanov
{"title":"On computable numberings of families of Turing degrees","authors":"Marat Faizrahmanov","doi":"10.1007/s00153-024-00914-9","DOIUrl":"10.1007/s00153-024-00914-9","url":null,"abstract":"<div><p>In this work, we study computable families of Turing degrees introduced and first studied by Arslanov and their numberings. We show that there exist finite families of Turing c.e. degrees both those with and without computable principal numberings and that every computable principal numbering of a family of Turing degrees is complete with respect to any element of the family. We also show that every computable family of Turing degrees has a complete with respect to each of its elements computable numbering even if it has no principal numberings. It follows from results by Mal’tsev and Ershov that complete numberings have nice programming tools and computational properties such as Kleene’s recursion theorems, Rice’s theorem, Visser’s ADN theorem, etc. Thus, every computable family of Turing degrees has a computable numbering with these properties. Finally, we prove that the Rogers semilattice of each such non-empty non-singleton family is infinite and is not a lattice.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 5-6","pages":"609 - 622"},"PeriodicalIF":0.3,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171806","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
Around accumulation points and maximal sequences of indiscernibles 堆积点周围和不可辨别的最大序列
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-03-13 DOI: 10.1007/s00153-024-00913-w
Moti Gitik
{"title":"Around accumulation points and maximal sequences of indiscernibles","authors":"Moti Gitik","doi":"10.1007/s00153-024-00913-w","DOIUrl":"10.1007/s00153-024-00913-w","url":null,"abstract":"<div><p>Answering a question of Mitchell (Trans Am Math Soc 329(2):507–530, 1992) we show that a limit of accumulation points can be singular in <span>({mathcal {K}})</span>. Some additional constructions are presented.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 5-6","pages":"591 - 608"},"PeriodicalIF":0.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00913-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129066","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
Varieties of truth definitions 真理定义的多样性
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-03-09 DOI: 10.1007/s00153-024-00909-6
Piotr Gruza, Mateusz Łełyk
{"title":"Varieties of truth definitions","authors":"Piotr Gruza,&nbsp;Mateusz Łełyk","doi":"10.1007/s00153-024-00909-6","DOIUrl":"10.1007/s00153-024-00909-6","url":null,"abstract":"<div><p>We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sentence <span>(alpha )</span> which extends a weak arithmetical theory (which we take to be <span>({{,mathrm{IDelta _{0}+exp },}})</span>) such that for some formula <span>(Theta )</span> and any arithmetical sentence <span>(varphi )</span>, <span>(Theta (ulcorner varphi urcorner )equiv varphi )</span> is provable in <span>(alpha )</span>. We say that a sentence <span>(beta )</span> is definable in a sentence <span>(alpha )</span>, if there exists an unrelativized translation from the language of <span>(beta )</span> to the language of <span>(alpha )</span> which is identity on the arithmetical symbols and such that the translation of <span>(beta )</span> is provable in <span>(alpha )</span>. Our main result is that the structure consisting of truth definitions which are conservative over the basic arithmetical theory forms a countable universal distributive lattice. Additionally, we generalize the result of Pakhomov and Visser showing that the set of (Gödel codes of) definitions of truth is not <span>(Sigma _2)</span>-definable in the standard model of arithmetic. We conclude by remarking that no <span>(Sigma _2)</span>-sentence, satisfying certain further natural conditions, can be a definition of truth for the language of arithmetic.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 5-6","pages":"563 - 589"},"PeriodicalIF":0.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099344","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
Essential hereditary undecidability 基本遗传不可判定性
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-03-01 DOI: 10.1007/s00153-024-00911-y
Albert Visser
{"title":"Essential hereditary undecidability","authors":"Albert Visser","doi":"10.1007/s00153-024-00911-y","DOIUrl":"10.1007/s00153-024-00911-y","url":null,"abstract":"<div><p>In this paper we study <i>essential hereditary undecidability</i>. Theories with this property are a convenient tool to prove undecidability of other theories. The paper develops the basic facts concerning essentially hereditary undecidability and provides salient examples, like a construction of essentially hereditarily undecidable theories due to Hanf and an example of a rather natural essentially hereditarily undecidable theory strictly below <span>R</span>. We discuss the (non-)interaction of essential hereditary undecidability with recursive boolean isomorphism. We develop a reduction relation <i>essential tolerance</i>, or, in the converse direction, <i>lax interpretability</i> that interacts in a good way with essential hereditary undecidability. We introduce the class of <span>(Sigma ^0_1)</span>-friendly theories and show that <span>(Sigma ^0_1)</span>-friendliness is sufficient but not necessary for essential hereditary undecidability. Finally, we adapt an argument due to Pakhomov, Murwanashyaka and Visser to show that there is no interpretability minimal essentially hereditarily undecidable theory.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 5-6","pages":"529 - 562"},"PeriodicalIF":0.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00911-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140017680","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
On the extendability to (mathbf {Pi }_3^0) ideals and Katětov order 关于向 $$mathbf {Pi }_3^0$$ 理想和 Katětov 秩的可扩展性
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-02-26 DOI: 10.1007/s00153-024-00912-x
Jialiang He, Jintao Luo, Shuguo Zhang
{"title":"On the extendability to (mathbf {Pi }_3^0) ideals and Katětov order","authors":"Jialiang He,&nbsp;Jintao Luo,&nbsp;Shuguo Zhang","doi":"10.1007/s00153-024-00912-x","DOIUrl":"10.1007/s00153-024-00912-x","url":null,"abstract":"<div><p>We show that there is a <span>( varvec{Sigma }_4^0)</span> ideal such that it’s neither extendable to any <span>( varvec{Pi }_3^0)</span> ideal nor above the ideal <span>( textrm{Fin}times textrm{Fin} )</span> in the sense of Katětov order, answering a question from M. Hrušák.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 5-6","pages":"523 - 528"},"PeriodicalIF":0.3,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979457","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
Errata: on the role of the continuum hypothesis in forcing principles for subcomplete forcing 勘误：关于连续体假设在次完全强迫原理中的作用
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-02-19 DOI: 10.1007/s00153-024-00905-w
Gunter Fuchs
{"title":"Errata: on the role of the continuum hypothesis in forcing principles for subcomplete forcing","authors":"Gunter Fuchs","doi":"10.1007/s00153-024-00905-w","DOIUrl":"10.1007/s00153-024-00905-w","url":null,"abstract":"<div><p>In this note, I will list instances where in the literature on subcomplete forcing and its forcing principles (mostly in articles of my own), the assumption of the continuum hypothesis, or that we are working above the continuum, was omitted. I state the correct statements and provide or point to correct proofs. There are also some new results, most of which revolve around showing the necessity of the extra assumption.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 5-6","pages":"509 - 521"},"PeriodicalIF":0.3,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139910639","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
Vector spaces with a union of independent subspaces 具有独立子空间联合的向量空间
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-02-17 DOI: 10.1007/s00153-024-00906-9
Alessandro Berarducci, Marcello Mamino, Rosario Mennuni
{"title":"Vector spaces with a union of independent subspaces","authors":"Alessandro Berarducci,&nbsp;Marcello Mamino,&nbsp;Rosario Mennuni","doi":"10.1007/s00153-024-00906-9","DOIUrl":"10.1007/s00153-024-00906-9","url":null,"abstract":"<div><p>We study the theory of <i>K</i>-vector spaces with a predicate for the union <i>X</i> of an infinite family of independent subspaces. We show that if <i>K</i> is infinite then the theory is complete and admits quantifier elimination in the language of <i>K</i>-vector spaces with predicates for the <i>n</i>-fold sums of <i>X</i> with itself. If <i>K</i> is finite this is no longer true, but we still have that a natural completion is near-model-complete.\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 3-4","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00906-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139902920","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
Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures 多项式有界 O 最小结构中有限阶全函数的不可定义性结果
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-02-15 DOI: 10.1007/s00153-024-00904-x
Hassan Sfouli
{"title":"Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures","authors":"Hassan Sfouli","doi":"10.1007/s00153-024-00904-x","DOIUrl":"10.1007/s00153-024-00904-x","url":null,"abstract":"<div><p>Let <span>({mathcal {R}})</span> be a polynomially bounded o-minimal expansion of the real field. Let <i>f</i>(<i>z</i>) be a transcendental entire function of finite order <span>(rho )</span> and type <span>(sigma in [0,infty ])</span>. The main purpose of this paper is to show that if (<span>(rho &lt;1)</span>) or (<span>(rho =1)</span> and <span>(sigma =0)</span>), the restriction of <i>f</i>(<i>z</i>) to the real axis is not definable in <span>({mathcal {R}})</span>. Furthermore, we give a generalization of this result for any <span>(rho in [0,infty ))</span>.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 3-4","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764772","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 second-order version of Morley’s theorem on the number of countable models does not require large cardinals 莫雷可数模型数定理的二阶版本不需要大的心形数
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-02-14 DOI: 10.1007/s00153-024-00907-8
Franklin D. Tall, Jing Zhang
{"title":"The second-order version of Morley’s theorem on the number of countable models does not require large cardinals","authors":"Franklin D. Tall,&nbsp;Jing Zhang","doi":"10.1007/s00153-024-00907-8","DOIUrl":"10.1007/s00153-024-00907-8","url":null,"abstract":"<div><p>The consistency of a second-order version of Morley’s Theorem on the number of countable models was proved in [EHMT23] with the aid of large cardinals. We here dispense with them.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 3-4","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764927","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
Indestructibility and the linearity of the Mitchell ordering 坚不可摧和米切尔排序的直线性
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-02-13 DOI: 10.1007/s00153-024-00908-7
Arthur W. Apter
{"title":"Indestructibility and the linearity of the Mitchell ordering","authors":"Arthur W. Apter","doi":"10.1007/s00153-024-00908-7","DOIUrl":"10.1007/s00153-024-00908-7","url":null,"abstract":"<div><p>Suppose that <span>(kappa )</span> is indestructibly supercompact and there is a measurable cardinal <span>(lambda &gt; kappa )</span>. It then follows that <span>(A_0 = {delta &lt; kappa mid delta )</span> is a measurable cardinal and the Mitchell ordering of normal measures over <span>(delta )</span> is nonlinear<span>(})</span> is unbounded in <span>(kappa )</span>. If the Mitchell ordering of normal measures over <span>(lambda )</span> is also linear, then by reflection (and without any use of indestructibility), <span>(A_1= {delta &lt; kappa mid delta )</span> is a measurable cardinal and the Mitchell ordering of normal measures over <span>(delta )</span> is linear<span>(})</span> is unbounded in <span>(kappa )</span> as well. The large cardinal hypothesis on <span>(lambda )</span> is necessary. We demonstrate this by constructing via forcing two models in which <span>(kappa )</span> is supercompact and <span>(kappa )</span> exhibits an indestructibility property slightly weaker than full indestructibility but sufficient to infer that <span>(A_0)</span> is unbounded in <span>(kappa )</span> if <span>(lambda &gt; kappa )</span> is measurable. In one of these models, for every measurable cardinal <span>(delta )</span>, the Mitchell ordering of normal measures over <span>(delta )</span> is linear. In the other of these models, for every measurable cardinal <span>(delta )</span>, the Mitchell ordering of normal measures over <span>(delta )</span> is nonlinear.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 3-4","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764739","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
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