Annals of Pure and Applied Logic最新文献_第8页

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

Strong minimal pairs in the enumeration degrees 枚举度中的强最小对

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-05-28 DOI: 10.1016/j.apal.2024.103464

Josiah Jacobsen-Grocott

引用次数: 0

Finite undecidability in PAC and PRC fields PAC 和 PRC 领域中的有限不可判定性

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-05-20 DOI: 10.1016/j.apal.2024.103465

Brian Tyrrell

引用次数: 0

Two-cardinal ideal operators and indescribability 双心理想算子与不可描述性

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-05-13 DOI: 10.1016/j.apal.2024.103463

Brent Cody , Philip White

引用次数: 0

Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal 巴赫曼-霍华德序数的基本序列和快速增长层次结构

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-05-13 DOI: 10.1016/j.apal.2024.103455

David Fernández-Duque, Andreas Weiermann

{"title":"Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal","authors":"David Fernández-Duque, Andreas Weiermann","doi":"10.1016/j.apal.2024.103455","DOIUrl":"10.1016/j.apal.2024.103455","url":null,"abstract":"<div>Hardy functions are defined by transfinite recursion and provide upper bounds for the growth rate of the provably total computable functions in various formal theories, making them an essential ingredient in many proofs of independence. Their definition is contingent on a choice of fundamental sequences, which approximate limits in a ‘canonical’ way. In order to ensure that these functions behave as expected, including the aforementioned unprovability results, these fundamental sequences must enjoy certain regularity properties.In this article, we prove that Buchholz's system of fundamental sequences for the ϑ function enjoys such conditions, including the Bachmann property. We partially extend these results to variants of the ϑ function, including a version without addition for countable ordinals. We conclude that the Hardy functions based on these notation systems enjoy natural monotonicity properties and majorize all functions defined by primitive recursion along <math><mi>ϑ</mi><mo>(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>Ω</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>)</mo></math>.</div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 8","pages":"Article 103455"},"PeriodicalIF":0.8,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168007224000538/pdfft?md5=a9318d0df651509a7116d53069683110&pid=1-s2.0-S0168007224000538-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061705","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

The ghosts of forgotten things: A study on size after forgetting 被遗忘事物的幽灵遗忘后的大小研究

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-05-08 DOI: 10.1016/j.apal.2024.103456

Paolo Liberatore

{"title":"The ghosts of forgotten things: A study on size after forgetting","authors":"Paolo Liberatore","doi":"10.1016/j.apal.2024.103456","DOIUrl":"10.1016/j.apal.2024.103456","url":null,"abstract":"<div>Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of reducing information, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is <math><msup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-hard in <math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math>. The same problem for unrestricted CNF propositional formulae is <math><msubsup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math>-hard in <math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math>.</div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 8","pages":"Article 103456"},"PeriodicalIF":0.8,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016800722400054X/pdfft?md5=664e39c8c02a1bed0bfc7e9414e88499&pid=1-s2.0-S016800722400054X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063991","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

Continuum many different things: Localisation, anti-localisation and Yorioka ideals 延续许多不同的东西：本地化、反本地化和赖冈理想

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-04-15 DOI: 10.1016/j.apal.2024.103453

Miguel A. Cardona , Lukas Daniel Klausner , Diego A. Mejía

引用次数: 0

Profiniteness, monadicity and universal models in modal logic 模态逻辑中的轮廓性、一元性和普遍模型

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-04-15 DOI: 10.1016/j.apal.2024.103454

Matteo De Berardinis, Silvio Ghilardi

引用次数: 0

Can you take Komjath's inaccessible away? 你能把科姆亚特无法进入的地方带走吗？

IF 0.8 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-04-15 DOI: 10.1016/j.apal.2024.103452

Hossein Lamei Ramandi , Stevo Todorcevic

{"title":"Can you take Komjath's inaccessible away?","authors":"Hossein Lamei Ramandi , Stevo Todorcevic","doi":"10.1016/j.apal.2024.103452","DOIUrl":"https://doi.org/10.1016/j.apal.2024.103452","url":null,"abstract":"<div>In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the effect of large cardinal assumptions on this comparison. Using the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains an Aronszajn subtree, if there is an inaccessible cardinal. This is stronger than Komjath's theorem in [5], where he proves the same consistency from two inaccessible cardinals. Moreover, we prove it is consistent with ZFC that there is a Kurepa tree T such that if <math><mi>U</mi><mo>⊂</mo><mi>T</mi></math> is a Kurepa tree with the inherited order from T, then U has an Aronszajn subtree. This theorem uses no large cardinal assumption. Our last theorem immediately implies the following: If <math><msub><mrow><mi>MA</mi></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub></math> holds and <math><msub><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msub></math> is not a Mahlo cardinal in <figure><img></figure> then there is a Kurepa tree with the property that every Kurepa subset has an Aronszajn subtree. Our work entails proving a new lemma about Todorcevic's ρ function which might be useful in other contexts.</div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 7","pages":"Article 103452"},"PeriodicalIF":0.8,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168007224000502/pdfft?md5=1993a5c4769b9c98665f24c8f3058ad9&pid=1-s2.0-S0168007224000502-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140632557","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