Annals of Pure and Applied Logic最新文献_第4页

Constructing models of small ordered theories with maximal countable spectrum 构造具有极大可数谱的小有序理论模型

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-02-01 Epub Date: 2025-10-01 DOI: 10.1016/j.apal.2025.103659

B. Baizhanov , T. Zambarnaya

引用次数: 0

Proof-theoretic investigation of λβ-reduction in the simply typed λ-calculus 单型λ微积分中λβ约简的证明理论研究

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-09-23 DOI: 10.1016/j.apal.2025.103657

William Stirton

引用次数: 0

Unified inverse correspondence for LE-logics le逻辑的统一逆对应

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-07-09 DOI: 10.1016/j.apal.2025.103635

Alessandra Palmigiano , Mattia Panettiere

引用次数: 0

Fundamental sequences based on localization 基于定位的基本序列

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-09-24 DOI: 10.1016/j.apal.2025.103658

Gunnar Wilken

{"title":"Fundamental sequences based on localization","authors":"Gunnar Wilken","doi":"10.1016/j.apal.2025.103658","DOIUrl":"10.1016/j.apal.2025.103658","url":null,"abstract":"<div><div>Building on Buchholz' assignment for ordinals below Bachmann-Howard ordinal, see <span><span>[2]</span></span>, we introduce systems of fundamental sequences for two kinds of relativized <em>ϑ</em>-function-based notation systems of strength <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></msubsup><msub><mrow><mi>-CA</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and prove Bachmann property for these systems, which is essential for monotonicity properties of subrecursive hierarchies defined on the basis of fundamental sequences. The central notion of our construction is the notion of <em>localization</em>, which was introduced in <span><span>[12]</span></span>.</div><div>The first kind of <em>stepwise defined ϑ</em>-functions over ordinal addition as basic function fits the framework of the ordinal arithmetical toolkit developed in <span><span>[12]</span></span>, whereas the second kind of <em>ϑ</em>-functions is defined <em>simultaneously</em> and will allow for further generalization to larger proof-theoretic ordinals, see <span><span>[10]</span></span>.</div><div>The systems of fundamental sequences given here enable the investigation of fundamental sequences and independence phenomena also in the context of patterns of resemblance, an approach to ordinal notations that is both semantic and combinatorial and was first introduced by Carlson in <span><span>[4]</span></span> and further analyzed in <span><span>[11]</span></span>, <span><span>[13]</span></span>, <span><span>[14]</span></span>, <span><span>[5]</span></span>.</div><div>Our exposition is put into the context of the abstract approach to fundamental sequences developed by Buchholz, Cichon, and Weiermann in <span><span>[3]</span></span>. The results of this paper will be applied to the theory of Goodstein sequences, extending results of <span><span>[7]</span></span>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 1","pages":"Article 103658"},"PeriodicalIF":0.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219605","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

Countable ordered groups and Weihrauch reducibility 可数有序群与Weihrauch可约性

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-07-25 DOI: 10.1016/j.apal.2025.103644

Ang Li

{"title":"Countable ordered groups and Weihrauch reducibility","authors":"Ang Li","doi":"10.1016/j.apal.2025.103644","DOIUrl":"10.1016/j.apal.2025.103644","url":null,"abstract":"<div><div>This paper continues to study the connection between reverse mathematics and Weihrauch reducibility. In particular, we study the problems formed from Maltsev's theorem <span><span>[11]</span></span> on the order types of countable ordered groups. Solomon <span><span>[14]</span></span> showed that the theorem is equivalent to <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>-<span><math><mi>C</mi><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the strongest of the big five subsystems of second order arithmetic. We show that the strength of the theorem comes from having a dense linear order without endpoints in its order type. Then, we show that for the related Weihrauch problem to be strong enough to be equivalent to <span><math><mover><mrow><mi>WF</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> (the analog problem of <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>-<span><math><mi>C</mi><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>), an order-preserving function is necessary in the output. Without the order-preserving function, the problems are very much to the side compared to analog problems of the big five.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 1","pages":"Article 103644"},"PeriodicalIF":0.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771199","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

Classifying different criteria for learning algebraic structures 分类学习代数结构的不同标准

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-08-22 DOI: 10.1016/j.apal.2025.103648

Nikolay Bazhenov , Vittorio Cipriani , Sanjay Jain , Luca San Mauro , Frank Stephan

{"title":"Classifying different criteria for learning algebraic structures","authors":"Nikolay Bazhenov , Vittorio Cipriani , Sanjay Jain , Luca San Mauro , Frank Stephan","doi":"10.1016/j.apal.2025.103648","DOIUrl":"10.1016/j.apal.2025.103648","url":null,"abstract":"<div><div>In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from a given target family and is required to output an hypothesis about the structure's isomorphism type. So far researchers focused on <strong>Ex</strong>-learning, in which the learner is asked to eventually stabilize to the correct hypothesis, and on restrictions where the learner is allowed to change the hypothesis a fixed number of times. Yet, other learning paradigms coming from classical algorithmic learning theory remained unexplored. We study the ‘‘learning power’’ of such criteria, comparing them via descriptive-set-theoretic tools thanks to the novel notion of <em>E</em>-learnability. The main outcome of this paper is that such criteria admit natural syntactic characterizations in terms of infinitary formulas analogous to the one given for <strong>Ex</strong>-learning in <span><span>[8]</span></span>. Such characterizations give a powerful method to understand whether a family of structures is learnable with respect to the desired criterion.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 1","pages":"Article 103648"},"PeriodicalIF":0.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903024","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

Thick sets and the Central Set Theorem 厚集与中心集定理

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-07-25 DOI: 10.1016/j.apal.2025.103645

Teng Zhang

引用次数: 0

Description of structures computable in polynomial time 在多项式时间内可计算的结构描述

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-07-16 DOI: 10.1016/j.apal.2025.103636

Pavel E. Alaev

引用次数: 0

Equivalence of multiset-based consequence relations 基于多集的结果关系的等价性

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-08-05 DOI: 10.1016/j.apal.2025.103646

Ali Madanshekaf , Adam Přenosil , Zeinab Khanjanzadeh Seresti , Constantine Tsinakis

引用次数: 0

Uncountable homogeneous structures 不可数同构结构

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-01-01 Epub Date: 2025-08-27 DOI: 10.1016/j.apal.2025.103649

Adam Bartoš, Wiesław Kubiś

引用次数: 0