Some variations on the splitting number

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-07-24 DOI:10.1016/j.apal.2023.103321

Saharon Shelah , Juris Steprāns

引用次数: 0

Abstract

Variations on the splitting number $s$ are examined by localizing the splitting property to finite sets. To be more precise, rather than considering families of subsets of the integers that have the property that every infinite set is split into two infinite sets by some member of the family a stronger property is considered: Whenever an subset of the integers is represented as the disjoint union of a family of finite sets one can ask that each of the finite sets is split into two non-empty pieces by some member of the family. It will be shown that restricting the size of the finite sets can result in distinguishable properties. In §2 some inequalities will be established, while in §3 the main consistency result will be proved.

查看原文本刊更多论文

关于分裂数的一些变化

通过将分裂性质定域到有限集，研究了分裂数s的变化。更精确地说，与其考虑具有每一个无限集都被一族成员分割成两个无限集的整数子集族，还不如考虑一个更强的性质:当整数的一个子集被表示为有限集合族的不相交并时，我们可以要求每一个有限集合都被一族成员分割成两个非空的部分。将证明限制有限集的大小可以导致可区分的性质。在§2里，我们将建立一些不等式，而在§3里，我们将证明主要的相合性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.