Annals of Pure and Applied Logic最新文献_第3页

Elimination of quantifiers for a theory of real closed rings 实闭环理论的量词消除

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-07-06 DOI: 10.1016/j.apal.2024.103494

Jorge I. Guier

引用次数: 0

Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence 用一个函数扩展的整数加法结构的模型完备性和可判定性的比蒂序列

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-07-06 DOI: 10.1016/j.apal.2024.103493

Mohsen Khani , Ali N. Valizadeh , Afshin Zarei

引用次数: 0

Club stationary reflection and other combinatorial principles at ℵω+2 ℵω+2处的俱乐部静止反射和其他组合原理

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-07-01 DOI: 10.1016/j.apal.2024.103489

引用次数: 0

Bi-intermediate logics of trees and co-trees 树和共树的双中间逻辑

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-07-01 DOI: 10.1016/j.apal.2024.103490

{"title":"Bi-intermediate logics of trees and co-trees","authors":"","doi":"10.1016/j.apal.2024.103490","DOIUrl":"10.1016/j.apal.2024.103490","url":null,"abstract":"<div>A bi-Heyting algebra validates the Gödel-Dummett axiom <math><mo>(</mo><mi>p</mi><mo>→</mo><mi>q</mi><mo>)</mo><mo>∨</mo><mo>(</mo><mi>q</mi><mo>→</mo><mi>p</mi><mo>)</mo></math> iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-Heyting algebras of this kind are called bi-Gödel algebras and form a variety that algebraizes the extension <math><mi>bi-GD</mi></math> of bi-intuitionistic logic axiomatized by the Gödel-Dummett axiom. In this paper we initiate the study of the lattice <math><mi>Λ</mi><mo>(</mo><mi>bi-GD</mi><mo>)</mo></math> of extensions of <math><mi>bi-GD</mi></math>.We develop the methods of Jankov-style formulas for bi-Gödel algebras and use them to prove that there are exactly continuum many extensions of <math><mi>bi-GD</mi></math>. We also show that all these extensions can be uniformly axiomatized by canonical formulas. Our main result is a characterization of the locally tabular extensions of <math><mi>bi-GD</mi></math>. We introduce a sequence of co-trees, called the finite combs, and show that a logic in <math><mi>Λ</mi><mo>(</mo><mi>bi-GD</mi><mo>)</mo></math> is locally tabular iff it contains at least one of the Jankov formulas associated with the finite combs. It follows that there exists the greatest nonlocally tabular extension of <math><mi>bi-GD</mi></math> and consequently, a unique pre-locally tabular extension of <math><mi>bi-GD</mi></math>. These results contrast with the case of the intermediate logic axiomatized by the Gödel-Dummett axiom, which is known to have only countably many extensions, all of which are locally tabular.</div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 10","pages":"Article 103490"},"PeriodicalIF":0.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168007224000940/pdfft?md5=c7604d9cf135b7d72a099447fc38fed7&pid=1-s2.0-S0168007224000940-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Searching problems above arithmetical transfinite recursion 搜索算术无穷递归以上的问题

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-06-19 DOI: 10.1016/j.apal.2024.103488

Yudai Suzuki , Keita Yokoyama

引用次数: 0

Decidability bounds for Presburger arithmetic extended by sine 由正弦扩展的普雷斯伯格算术的可判定性边界

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-06-12 DOI: 10.1016/j.apal.2024.103487

引用次数: 0

From GTC to : Generating reset proof systems from cyclic proof systems 从 GTC 到：从循环证明系统生成重置证明系统

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-06-11 DOI: 10.1016/j.apal.2024.103485

Graham E. Leigh, Dominik Wehr

{"title":"From GTC to : Generating reset proof systems from cyclic proof systems","authors":"Graham E. Leigh, Dominik Wehr","doi":"10.1016/j.apal.2024.103485","DOIUrl":"10.1016/j.apal.2024.103485","url":null,"abstract":"<div>We consider cyclic proof systems in which derivations are graphs rather than trees. Such systems typically come with a condition that isolates which derivations are admitted as proofs, known as the soundness condition. This soundness condition frequently takes the form of either a global trace condition, a property dependent on all infinite paths in the proof-graph, or a reset condition, a ‘local’ condition depending on the simple cycles only which, as a result, is typically stable under more proof transformations.In this article we present a general method for constructing cyclic proof systems with reset conditions from systems with global trace conditions. In contrast to previous approaches, this method of generation is entirely independent of logic's semantics, only relying on combinatorial aspects of the notion of ‘trace’ and ‘progress’. We apply this method to present reset proof systems for three cyclic proof systems from the literature: cyclic arithmetic, cyclic Gödel's T and cyclic tableaux for the modal μ-calculus.</div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 10","pages":"Article 103485"},"PeriodicalIF":0.6,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168007224000897/pdfft?md5=3f6516f2a534f0fa710275ea2d71b171&pid=1-s2.0-S0168007224000897-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141402450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Posets of copies of countable ultrahomogeneous tournaments 可数超均质锦标赛副本的 Posets

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-06-06 DOI: 10.1016/j.apal.2024.103486

Miloš S. Kurilić , Stevo Todorčević

引用次数: 0

Around definable types in p-adically closed fields 围绕 p-adically 闭域中的可定义类型

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-06-04 DOI: 10.1016/j.apal.2024.103484

Pablo Andújar Guerrero , Will Johnson

{"title":"Around definable types in p-adically closed fields","authors":"Pablo Andújar Guerrero , Will Johnson","doi":"10.1016/j.apal.2024.103484","DOIUrl":"https://doi.org/10.1016/j.apal.2024.103484","url":null,"abstract":"<div>We prove some technical results on definable types in p-adically closed fields, with consequences for definable groups and definable topological spaces. First, the code of a definable n-type (in the field sort) can be taken to be a real tuple (in the field sort) rather than an imaginary tuple (in the geometric sorts). Second, any definable type in the real or imaginary sorts is generated by a countable union of chains parameterized by the value group. Third, if X is an interpretable set, then the space of global definable types on X is strictly pro-interpretable, building off work of Cubides Kovacsics, Hils, and Ye [7], [8]. Fourth, global definable types can be lifted (in a non-canonical way) along interpretable surjections. Fifth, if G is a definable group with definable f-generics (dfg), and G acts on a definable set X, then the quotient space <math><mi>X</mi><mo>/</mo><mi>G</mi></math> is definable, not just interpretable. This explains some phenomena observed by Pillay and Yao [24]. Lastly, we show that interpretable topological spaces satisfy analogues of first-countability and curve selection. Using this, we show that all reasonable notions of definable compactness agree on interpretable topological spaces, and that definable compactness is definable in families.</div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 10","pages":"Article 103484"},"PeriodicalIF":0.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141325305","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

Forcing axioms and the uniformization-property 强制公理和统一化属性

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-05-29 DOI: 10.1016/j.apal.2024.103466

Stefan Hoffelner

引用次数: 0