Annals of Pure and Applied Logic最新文献_第2页

A note on Erdős-Hajnal property for graphs with VC dimension ≤2 关于VC维≤2图Erdős-Hajnal性质的注解

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2025-12-16 DOI: 10.1016/j.apal.2025.103705

Yayi Fu

引用次数: 0

Constructibility real degrees in the side-by-side Sacks model 并行Sacks模型的可构造性实数

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-05-01 Epub Date: 2026-01-08 DOI: 10.1016/j.apal.2026.103722

Lorenzo Notaro

引用次数: 0

Preserving and constructing multiple gaps 保留和建造多个缺口

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.2026.103721

Osvaldo Guzmán , Francisco Santiago Nieto-de la Rosa

引用次数: 0

Maximal sets without choice 无选择的极大集

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-04-01 Epub Date: 2025-11-27 DOI: 10.1016/j.apal.2025.103694

Jonathan Schilhan

{"title":"Maximal sets without choice","authors":"Jonathan Schilhan","doi":"10.1016/j.apal.2025.103694","DOIUrl":"10.1016/j.apal.2025.103694","url":null,"abstract":"<div><div>We show that it is consistent relative to <math><mi>ZF</mi></math>, that there is no well-ordering of <math><mi>R</mi></math> while a wide class of special sets of reals such as Hamel bases, transcendence bases, Vitali sets or Bernstein sets exists. To be more precise, we can assume that every projective hypergraph on <math><mi>R</mi></math> has a maximal independent set, among a few other things. For example, we get transversals for all projective equivalence relations. Moreover, this is possible while either <math><msub><mrow><mi>DC</mi></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></math> holds, or countable choice for reals fails. Assuming the consistency of an inaccessible cardinal, “projective” can even be replaced with “<math><mi>L</mi><mo>(</mo><mi>R</mi><mo>)</mo></math>” and we can add that any instance of <math><mi>AC</mi></math> in <math><mi>L</mi><mo>(</mo><mi>R</mi><mo>)</mo></math> has a choice function. This vastly strengthens the consistency results obtained in [6], [11] or [15].</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 4","pages":"Article 103694"},"PeriodicalIF":0.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694156","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 existence and disjunction properties in structural set theory 结构集论中的存在性和析取性

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-04-01 Epub Date: 2025-11-19 DOI: 10.1016/j.apal.2025.103683

Mark Saving

引用次数: 0

Exponential topological fields with a generic derivation 具有一般推导的指数拓扑域

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-04-01 Epub Date: 2025-11-19 DOI: 10.1016/j.apal.2025.103682

Françoise Point , Nathalie Regnault

引用次数: 0

Twin procedures, two kinds of variable binding, and two kinds of computation 双过程，两种变量绑定，两种计算

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-04-01 Epub Date: 2025-11-27 DOI: 10.1016/j.apal.2025.103693

Marie Duží , Bjørn Jespersen

{"title":"Twin procedures, two kinds of variable binding, and two kinds of computation","authors":"Marie Duží , Bjørn Jespersen","doi":"10.1016/j.apal.2025.103693","DOIUrl":"10.1016/j.apal.2025.103693","url":null,"abstract":"<div><div>We address and solve some technical problems arising in Transparent Intensional Logic, which identifies hyperintensions with algorithmically structured procedures. The problems concern variable binding and substitution. A pair of procedures, called Trivialization and Double Execution, work together well in most cases. But there are limiting cases where they fail to. Trivialization, if applied to another procedure, makes it feasible to operate on this procedure itself rather than on the product it is typed and structured to yield. Any occurrences of variables within the procedure become Trivialization-bound. Trivialization-binding is stronger than λ-binding. Double Execution, when applied to another procedure, is typed and structured to, first, obtain the product of this procedure and, second, obtain the product of this product on condition that the latter is itself a procedure. Double Execution can turn some Trivialization-bound occurrences of variables into free occurrences, and Double Execution may also produce fresh variables. Such cases undermine our definition of substitution, thus jeopardizing the validity of the rules of λ-conversion. The restrictions required are obtained by revising fundamental definitions. The problem we address and solve extends beyond Transparent Intensional Logic. Any logic or programming language (especially if based on the λ-calculus) furnished with a high degree of expressive power, in which procedures can occur as operands, is liable to confront similar problems.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 4","pages":"Article 103693"},"PeriodicalIF":0.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797266","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

Construction schemes: Transferring structures from ω to ω1 结构方案：ω向ω1转换

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-04-01 Epub Date: 2025-11-11 DOI: 10.1016/j.apal.2025.103679

Jorge Antonio Cruz Chapital, Osvaldo Guzmán González, Stevo Todorčević

引用次数: 0

Green points in the reals 现实中的绿点

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-03-01 Epub Date: 2025-10-21 DOI: 10.1016/j.apal.2025.103666

Yilong Zhang

引用次数: 0

Isolated d.c.e. degrees and Σ1 induction 隔离直流度和Σ1感应

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2026-03-01 Epub Date: 2025-11-10 DOI: 10.1016/j.apal.2025.103678

Yiqun Liu , Yong Liu , Cheng Peng

{"title":"Isolated d.c.e. degrees and Σ1 induction","authors":"Yiqun Liu , Yong Liu , Cheng Peng","doi":"10.1016/j.apal.2025.103678","DOIUrl":"10.1016/j.apal.2025.103678","url":null,"abstract":"<div><div>A Turing degree is d.c.e. if it contains a set that is the difference of two c.e. sets. A d.c.e. degree d is isolated by a c.e. degree <math><mi>a</mi><mo><</mo><mi>d</mi></math> if all c.e. degrees that are below d are also below a; d is isolated from above by a c.e. degree <math><mi>a</mi><mo>></mo><mi>d</mi></math> if all c.e. degrees that are above d are also above a. In this paper, we study the inductive strength of both isolated and upper isolated d.c.e. degrees from the point of view of reverse recursion theory. We show that (1) <math><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>+</mo><mi>B</mi><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mtext>Exp</mtext><mo>⊢</mo><mi>I</mi><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>↔</mo></math> There is an isolated proper d.c.e. degree below <math><msup><mrow><mn>0</mn></mrow><mrow><mo>′</mo></mrow></msup></math>; (2) <math><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>+</mo><mi>B</mi><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mtext>Exp</mtext><mo>⊢</mo><mi>I</mi><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>↔</mo></math> There is an upper isolated proper d.c.e. degree below <math><msup><mrow><mn>0</mn></mrow><mrow><mo>′</mo></mrow></msup></math>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"177 3","pages":"Article 103678"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528622","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