发布求助
文献互助 智能选刊 最新文献

Annals of Pure and Applied Logic最新文献

筛选
英文 中文
Pathologies in satisfaction classes 满意度课的病理学
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-20 DOI: 10.1016/j.apal.2023.103387
Athar Abdul-Quader , Mateusz Łełyk
{"title":"Pathologies in satisfaction classes","authors":"Athar Abdul-Quader ,&nbsp;Mateusz Łełyk","doi":"10.1016/j.apal.2023.103387","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103387","url":null,"abstract":"<div><p>We study subsets of countable recursively saturated models of <span><math><mi>PA</mi></math></span> which can be defined using pathologies in satisfaction classes. More precisely, we characterize those subsets <em>X</em> such that there is a satisfaction class <em>S</em> where <em>S</em> behaves correctly on an idempotent disjunction of length <em>c</em> if and only if <span><math><mi>c</mi><mo>∈</mo><mi>X</mi></math></span>. We generalize this result to characterize several types of pathologies including double negations, blocks of extraneous quantifiers, and binary disjunctions and conjunctions. We find a surprising relationship between the cuts which can be defined in this way and arithmetic saturation: namely, a countable nonstandard model is arithmetically saturated if and only if every cut can be the “idempotent disjunctively correct cut” in some satisfaction class. We describe the relationship between types of pathologies and the closure properties of the cuts defined by these pathologies.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 2","pages":"Article 103387"},"PeriodicalIF":0.8,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49725035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On the geometric equivalence of algebras 代数的几何等价性
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-06 DOI: 10.1016/j.apal.2023.103386
M. Shahryari
{"title":"On the geometric equivalence of algebras","authors":"M. Shahryari","doi":"10.1016/j.apal.2023.103386","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103386","url":null,"abstract":"<div><p>It is known that an algebra is geometrically equivalent to any of its filterpowers if it is <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-compact. We present an explicit description for the radicals of systems of equation over an algebra <em>A</em> and then we prove the above assertion by an elementary new argument. Then we define <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>κ</mi></mrow></msub></math></span>-compact algebras and <em>κ</em>-filterpowers for any infinite cardinal <em>κ</em>. We show that any <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>κ</mi></mrow></msub></math></span>-compact algebra is geometric equivalent to its <em>κ</em>-filterpowers. As there is no algebraic description of the <em>κ</em>-quasivariety generated by an algebra, the classical argument can not be applied in this case, while our proof still works.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 2","pages":"Article 103386"},"PeriodicalIF":0.8,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49725032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Social welfare relations and irregular sets 社会福利关系和不规则设置
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103302
Ram Sewak Dubey , Giorgio Laguzzi
{"title":"Social welfare relations and irregular sets","authors":"Ram Sewak Dubey ,&nbsp;Giorgio Laguzzi","doi":"10.1016/j.apal.2023.103302","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103302","url":null,"abstract":"<div><p>Social welfare relations satisfying Pareto and equity principles on infinite utility streams have revealed a non-constructive nature, specifically by showing that in general they imply the existence of non-Ramsey sets and non-Lebesgue measurable sets. In <span>[4, Problem 11.14]</span>, the authors ask whether such a connection holds with non-Baire sets as well. In this paper we answer such a question showing that several versions of Pareto principles acting on different utility domains imply the existence of non-Baire sets. Furthermore, we analyze in more details the needed fragments of AC and we start a systematic investigation of a <em>social welfare diagram</em> in a similar fashion done in the past decades concerning cardinal invariants and regularity properties of the reals. In doing that we use tools from forcing theory, such as specific tree-forcings (in particular variants of Silver and Mathias forcings) and Shelah's amalgamation.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103302"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49754694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Krull dimension in set theory 集合论中的库尔维数
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103299
Jindřich Zapletal
{"title":"Krull dimension in set theory","authors":"Jindřich Zapletal","doi":"10.1016/j.apal.2023.103299","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103299","url":null,"abstract":"<div><p>For every number <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, let <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be the hypergraph on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> of arity four consisting of all non-degenerate Euclidean rectangles. It is consistent with ZF+DC set theory that the chromatic number of <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is countable while that of <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> is not.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103299"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49754695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 3
Carlson-Simpson's lemma and applications in reverse mathematics 卡尔森-辛普森引理及其在逆向数学中的应用
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103287
Paul-Elliot Angles d'Auriac , Lu Liu , Bastien Mignoty , Ludovic Patey
{"title":"Carlson-Simpson's lemma and applications in reverse mathematics","authors":"Paul-Elliot Angles d'Auriac ,&nbsp;Lu Liu ,&nbsp;Bastien Mignoty ,&nbsp;Ludovic Patey","doi":"10.1016/j.apal.2023.103287","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103287","url":null,"abstract":"<div><p>We study the reverse mathematics of infinitary extensions of the Hales-Jewett theorem, due to Carlson and Simpson. These theorems have multiple applications in Ramsey's theory, such as the existence of finite big Ramsey degrees for the triangle-free graph, or the Dual Ramsey theorem. We show in particular that the Open Dual Ramsey theorem holds in <span><math><msubsup><mrow><mi>ACA</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msubsup></math></span>.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103287"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49754698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Lipschitz and Wadge binary games in second order arithmetic 二阶算术的Lipschitz和Wadge二进制对策
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103301
Andrés Cordón-Franco , F. Félix Lara-Martín , Manuel J.S. Loureiro
{"title":"Lipschitz and Wadge binary games in second order arithmetic","authors":"Andrés Cordón-Franco ,&nbsp;F. Félix Lara-Martín ,&nbsp;Manuel J.S. Loureiro","doi":"10.1016/j.apal.2023.103301","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103301","url":null,"abstract":"<div><p>We present a detailed formalization of Lipschitz and Wadge games in the context of second order arithmetic and we investigate the logical strength of Lipschitz and Wadge determinacy, and the tightly related Semi-Linear Ordering principle, for the first levels of the Hausdorff difference hierarchy in the Cantor space. As a result, we obtain characterizations of <span><math><msub><mrow><mi>WKL</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>ACA</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> in terms of these determinacy principles.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103301"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49754697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Choice and independence of premise rules in intuitionistic set theory 直觉集合论中前提规则的选择与独立性
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103314
Emanuele Frittaion , Takako Nemoto , Michael Rathjen
{"title":"Choice and independence of premise rules in intuitionistic set theory","authors":"Emanuele Frittaion ,&nbsp;Takako Nemoto ,&nbsp;Michael Rathjen","doi":"10.1016/j.apal.2023.103314","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103314","url":null,"abstract":"<div><p>Choice and independence of premise principles play an important role in characterizing Kreisel's modified realizability and Gödel's Dialectica interpretation. In this paper we show that a great many intuitionistic set theories are closed under the corresponding rules for finite types over <span><math><mi>N</mi></math></span>. It is also shown that the existence property (or existential definability property) holds for statements of the form <span><math><mo>∃</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>σ</mi></mrow></msup><mspace></mspace><mi>φ</mi><mo>(</mo><mi>y</mi><mo>)</mo></math></span>, where the variable <em>y</em> ranges over objects of finite type <em>σ</em>. This applies in particular to <span><math><mi>CZF</mi></math></span> (Constructive Zermelo-Fraenkel set theory) and <span><math><mi>IZF</mi></math></span> (Intuitionistic Zermelo-Fraenkel set theory), two systems known not to have the general existence property. On the technical side, the paper uses a method that amalgamates generic realizability for set theory with truth, whereby the underlying partial combinatory algebra is required to <em>contain</em> all objects of finite type.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103314"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49754702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Alternatives to the Halpern-Läuchli theorem Halpern-Läuchli定理的替代方案
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103313
Nedeljko Stefanović
{"title":"Alternatives to the Halpern-Läuchli theorem","authors":"Nedeljko Stefanović","doi":"10.1016/j.apal.2023.103313","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103313","url":null,"abstract":"<div><p>In this paper, it is shown that the fact that the BPI holds in the Cohen's symmetric model can be used as an equal substitute for the Halpern-Läuchli theorem. Also, some alternatives to the Halpern-Läuchli theorem in the form of absoluteness theorems for a certain class of statements are consequences<span><sup>1</sup></span> of such consistency results. The article also contains a new proof of the Halpern-Läuchli theorem.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103313"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49754701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
An undecidable extension of Morley's theorem on the number of countable models 莫雷定理关于可数模型数的不可定推广
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103317
Christopher J. Eagle , Clovis Hamel , Sandra Müller , Franklin D. Tall
{"title":"An undecidable extension of Morley's theorem on the number of countable models","authors":"Christopher J. Eagle ,&nbsp;Clovis Hamel ,&nbsp;Sandra Müller ,&nbsp;Franklin D. Tall","doi":"10.1016/j.apal.2023.103317","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103317","url":null,"abstract":"<div><p>We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103317"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49724344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Halfway new cardinal characteristics 半新基本特征
IF 0.8 2区 数学
Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103303
Jörg Brendle , Lorenz J. Halbeisen , Lukas Daniel Klausner , Marc Lischka , Saharon Shelah
{"title":"Halfway new cardinal characteristics","authors":"Jörg Brendle ,&nbsp;Lorenz J. Halbeisen ,&nbsp;Lukas Daniel Klausner ,&nbsp;Marc Lischka ,&nbsp;Saharon Shelah","doi":"10.1016/j.apal.2023.103303","DOIUrl":"https://doi.org/10.1016/j.apal.2023.103303","url":null,"abstract":"<div><p>Based on the well-known cardinal characteristics <span><math><mi>s</mi></math></span>, <span><math><mi>r</mi></math></span> and <span><math><mi>i</mi></math></span>, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e.g. the consistency of <span><math><mi>s</mi><mo>&lt;</mo><msub><mrow><mi>s</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></math></span>, as well as several results about possible values of <span><math><msub><mrow><mi>i</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></math></span>.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"174 9","pages":"Article 103303"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49754699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 3
首页 上一页
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