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
On classification of continuous first order theories 关于连续一阶理论的分类
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-07-01 Epub Date: 2026-02-02 DOI: 10.1016/j.apal.2026.103729
Karim Khanaki
{"title":"On classification of continuous first order theories","authors":"Karim Khanaki","doi":"10.1016/j.apal.2026.103729","DOIUrl":"10.1016/j.apal.2026.103729","url":null,"abstract":"<div><div>We present several new characterizations of <em>IP</em> (the independence property) and <em>SOP</em> (the strict order property) for continuous first-order logic and explore their connections to functional analysis and Banach space theory. Furthermore, we propose new dividing lines for unstable theories by examining subclasses of Baire-1 functions. We also explain why one should not expect a perfect analogue of Shelah's theorem—namely, that a theory is unstable if and only if it has <em>IP</em> or <em>SOP</em>—to hold for real-valued logics, particularly in the context of continuous logic.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 7","pages":"Article 103729"},"PeriodicalIF":0.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116732","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 algebraic sums, trees and ideals in the Cantor space 关于康托空间中的代数和、树和理想
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-06-01 Epub Date: 2026-01-12 DOI: 10.1016/j.apal.2026.103724
Marcin Michalski, Robert Rałowski, Szymon Żeberski
{"title":"On algebraic sums, trees and ideals in the Cantor space","authors":"Marcin Michalski,&nbsp;Robert Rałowski,&nbsp;Szymon Żeberski","doi":"10.1016/j.apal.2026.103724","DOIUrl":"10.1016/j.apal.2026.103724","url":null,"abstract":"<div><div>We work in the Cantor space <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>ω</mi></mrow></msup></math></span>. The results of the paper adhere to the following pattern. Let <span><math><mi>I</mi><mo>∈</mo><mo>{</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>∩</mo><mi>N</mi><mo>,</mo><mi>E</mi><mo>}</mo></math></span> and <em>T</em> be a perfect, uniformly perfect or Silver tree. Then for every <span><math><mi>A</mi><mo>∈</mo><mi>I</mi></math></span> there exists <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>⊆</mo><mi>T</mi></math></span> of the same kind as <em>T</em> such that <span><math><mi>A</mi><mo>+</mo><munder><munder><mrow><mo>[</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>]</mo><mo>+</mo><mo>[</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>]</mo><mo>+</mo><mo>…</mo><mo>+</mo><mo>[</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>]</mo></mrow><mo>︸</mo></munder><mrow><mi>n</mi><mtext>–times</mtext></mrow></munder><mo>∈</mo><mi>I</mi></math></span> for each <span><math><mi>n</mi><mo>∈</mo><mi>ω</mi></math></span>. We also prove weaker statements for splitting trees. For the case <span><math><mi>E</mi></math></span> we also provide a simple characterization of a basis of <span><math><mi>E</mi></math></span>. We use these results to prove that the algebraic sum of a generalized Luzin set and a generalized Sierpiński set belongs to <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, provided that <span><math><mi>c</mi></math></span> is a regular cardinal.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 6","pages":"Article 103724"},"PeriodicalIF":0.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024445","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
Positively closed Sh(B)-valued models 正闭Sh(B)值模型
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-06-01 Epub Date: 2026-01-28 DOI: 10.1016/j.apal.2026.103726
Kristóf Kanalas
{"title":"Positively closed Sh(B)-valued models","authors":"Kristóf Kanalas","doi":"10.1016/j.apal.2026.103726","DOIUrl":"10.1016/j.apal.2026.103726","url":null,"abstract":"<div><div>We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a local notion (it only concerns the definable sets inside the model). For <strong>Set</strong>-valued models of coherent theories they coincide.</div><div>We prove that if <span><math><mi>E</mi><mo>=</mo><mi>S</mi><mi>h</mi><mo>(</mo><mi>B</mi><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>h</mi></mrow></msub><mo>)</mo></math></span> for a complete Boolean algebra, then positively closed but not strongly positively closed <span><math><mi>E</mi></math></span>-valued models of coherent theories exist, yet, there is an alternative local property which characterizes positively closed <span><math><mi>E</mi></math></span>-valued models.</div><div>A large part of our discussion is given in the context of infinite quantifier geometric logic, dealing with the fragment <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>κ</mi><mi>κ</mi></mrow><mrow><mi>g</mi></mrow></msubsup></math></span> where <em>κ</em> is weakly compact.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 6","pages":"Article 103726"},"PeriodicalIF":0.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079688","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
Amorphous sets and dual Dedekind finiteness 无定形集与对偶Dedekind有限性
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-06-01 Epub Date: 2026-01-08 DOI: 10.1016/j.apal.2026.103723
Yifan Hu , Ruihuan Mao , Guozhen Shen
{"title":"Amorphous sets and dual Dedekind finiteness","authors":"Yifan Hu ,&nbsp;Ruihuan Mao ,&nbsp;Guozhen Shen","doi":"10.1016/j.apal.2026.103723","DOIUrl":"10.1016/j.apal.2026.103723","url":null,"abstract":"<div><div>A set <em>A</em> is dually Dedekind finite if every surjection from <em>A</em> onto <em>A</em> is injective; otherwise, <em>A</em> is dually Dedekind infinite. An amorphous set is an infinite set that cannot be partitioned into two infinite subsets. A strictly amorphous set is an amorphous set in which every partition has only finitely many non-singleton blocks. It is proved consistent with <span><math><mi>ZF</mi></math></span> (i.e., Zermelo–Fraenkel set theory without the axiom of choice) that there exists an amorphous set <em>A</em> whose power set <span><math><mi>P</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is dually Dedekind infinite, which gives a negative solution to a question proposed by Truss (1974) <span><span>[13]</span></span>. Nevertheless, we prove in <span><math><mi>ZF</mi></math></span> that, for all strictly amorphous sets <em>A</em> and all natural numbers <em>n</em>, <span><math><mi>P</mi><msup><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup></math></span> is dually Dedekind finite, which generalizes a result of Goldstern.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 6","pages":"Article 103723"},"PeriodicalIF":0.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950127","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
The computational content of multidimensional discontinuity 多维不连续的计算内容
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.apal.2026.103720
Rupert Hölzl , Keng Meng Ng
{"title":"The computational content of multidimensional discontinuity","authors":"Rupert Hölzl ,&nbsp;Keng Meng Ng","doi":"10.1016/j.apal.2026.103720","DOIUrl":"10.1016/j.apal.2026.103720","url":null,"abstract":"<div><div>The Weihrauch degrees are a tool to gauge the computational difficulty of mathematical problems. Often, what makes these problems hard is their discontinuity. We look at discontinuity in its purest form, that is, at otherwise constant functions that make a single discontinuous step along each dimension of their underlying space. This is an extension of previous work of Kihara, Pauly, Westrick from a single dimension to multiple dimensions. Among other results, we obtain strict hierarchies in the Weihrauch degrees, one of which orders mathematical problems by the richness of the truth-tables determining how discontinuous steps influence the output.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 5","pages":"Article 103720"},"PeriodicalIF":0.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188106","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
Generic torsion-free groups and Rubin actions 一般无扭群和鲁宾作用
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2025-12-05 DOI: 10.1016/j.apal.2025.103704
Thomas Koberda, Yash Lodha
{"title":"Generic torsion-free groups and Rubin actions","authors":"Thomas Koberda,&nbsp;Yash Lodha","doi":"10.1016/j.apal.2025.103704","DOIUrl":"10.1016/j.apal.2025.103704","url":null,"abstract":"<div><div>We use model theoretic forcing to prove that a generic countable torsion-free group does not admit any non-trivial locally moving action on a Hausdorff topological space, and yet admits a rich Rubin poset.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 5","pages":"Article 103704"},"PeriodicalIF":0.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738714","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
Groups elementarily equivalent to metabelian Baumslag – Solitar groups and regular bi-interpretability 群基本等价于平衡的Baumslag - Solitar群和正则双可解释性
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2025-12-02 DOI: 10.1016/j.apal.2025.103695
Evelina Daniyarova , Alexei Myasnikov
{"title":"Groups elementarily equivalent to metabelian Baumslag – Solitar groups and regular bi-interpretability","authors":"Evelina Daniyarova ,&nbsp;Alexei Myasnikov","doi":"10.1016/j.apal.2025.103695","DOIUrl":"10.1016/j.apal.2025.103695","url":null,"abstract":"<div><div>We prove that metabelian Baumslag<!--> <!-->–<!--> <!-->Solitar group <span><math><mrow><mi>BS</mi></mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>)</mo></math></span>, <span><math><mi>k</mi><mo>&gt;</mo><mn>1</mn></math></span>, is (strongly) regularly bi-interpretable with the ring of integers <span><math><mi>Z</mi></math></span>, and describe in algebraic terms all groups that are elementarily equivalent to <span><math><mrow><mi>BS</mi></mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 5","pages":"Article 103695"},"PeriodicalIF":0.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145658449","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
Constructive quantifier elimination with a focus on matrix rings 以矩阵环为重点的建设性量词消去
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2025-12-22 DOI: 10.1016/j.apal.2025.103706
Max Illmer, Tim Netzer
{"title":"Constructive quantifier elimination with a focus on matrix rings","authors":"Max Illmer,&nbsp;Tim Netzer","doi":"10.1016/j.apal.2025.103706","DOIUrl":"10.1016/j.apal.2025.103706","url":null,"abstract":"<div><div>We give a sufficient condition for a model theoretic structure <em>B</em> to ‘inherit’ quantifier elimination from another structure <em>A</em>. This yields an alternative proof of one of the main results from <span><span>[8]</span></span>, namely quantifier elimination for certain matrix rings. The original proof uses model theory, and while it is very elegant and insightful, the proof we propose is much shorter and provides a constructive algorithm.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 5","pages":"Article 103706"},"PeriodicalIF":0.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884440","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
Algebraic independence of the solutions of the classical Lotka-Volterra system 经典Lotka-Volterra系统解的代数独立性
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2026-01-02 DOI: 10.1016/j.apal.2025.103707
Yutong Duan, Joel Nagloo
{"title":"Algebraic independence of the solutions of the classical Lotka-Volterra system","authors":"Yutong Duan,&nbsp;Joel Nagloo","doi":"10.1016/j.apal.2025.103707","DOIUrl":"10.1016/j.apal.2025.103707","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo><mo>…</mo><mo>,</mo><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> be distinct non-constant and non-degenerate solutions of the classical Lotka-Volterra system<span><span><span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>a</mi><mi>x</mi><mi>y</mi><mo>+</mo><mi>b</mi><mi>x</mi><mspace></mspace><msup><mrow><mi>y</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>c</mi><mi>x</mi><mi>y</mi><mo>+</mo><mi>d</mi><mi>y</mi></math></span></span></span> where <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>∈</mo><mi>C</mi><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span>. We show that if <em>d</em> and <em>b</em> are linearly independent over <span><math><mi>Q</mi></math></span>, then the solutions are algebraically independent over <span><math><mi>C</mi></math></span>, that is <span><math><mi>t</mi><mi>r</mi><mo>.</mo><mi>d</mi><mi>e</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>C</mi></mrow></msub><mi>C</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>2</mn><mi>n</mi></math></span>. As a main part of the proof, we show that the set defined by the system in universal differential fields, with <em>d</em> and <em>b</em> linearly independent over <span><math><mi>Q</mi></math></span>, is strongly minimal and geometrically trivial. Our techniques also allows us to obtain partial results for some of the more general 2<em>d</em>-Lotka-Volterra system.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 5","pages":"Article 103707"},"PeriodicalIF":0.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926009","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
The category dichotomy for ideals 理想的范畴二分法
IF 0.6 2区 数学
Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2026-01-07 DOI: 10.1016/j.apal.2025.103717
Alan Dow , Raúl Figueroa-Sierra , Osvaldo Guzmán , Michael Hrušák
{"title":"The category dichotomy for ideals","authors":"Alan Dow ,&nbsp;Raúl Figueroa-Sierra ,&nbsp;Osvaldo Guzmán ,&nbsp;Michael Hrušák","doi":"10.1016/j.apal.2025.103717","DOIUrl":"10.1016/j.apal.2025.103717","url":null,"abstract":"<div><div>We prove that there is an ideal on <em>ω</em> that is not Katětov below <span>nwd</span> and does not have restrictions above <span><math><mi>ED</mi></math></span>. We also prove that in the Laver model every tall <span>P</span>-ideal is Katětov-Blass above <span><math><msub><mrow><mi>ED</mi></mrow><mrow><mtext>fin</mtext></mrow></msub></math></span> and that it is consistent that every <span>Q</span><sup>+</sup> ideal is meager.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 5","pages":"Article 103717"},"PeriodicalIF":0.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976652","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
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：604180095
Book学术官方微信
小红书