Universally Sacks-indestructible combinatorial families of reals

IF 0.6 2区 数学 Q2 LOGIC
V. Fischer , L. Schembecker
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引用次数: 0

Abstract

We introduce the notion of an arithmetical type of combinatorial family of reals, which serves to generalize different types of families such as mad families, maximal cofinitary groups, ultrafilter bases, splitting families and other similar types of families commonly studied in combinatorial set theory.
We then prove that every combinatorial family of reals of arithmetical type which is indestructible by the product of Sacks forcing S0 is in fact universally Sacks-indestructible, i.e. it is indestructible by any countably supported iteration or product of Sacks-forcing of any length. Further, under CH we present a unified construction of universally Sacks-indestructible families for various arithmetical types of families. In particular we prove the existence of a universally Sacks-indestructible maximal cofinitary group under CH.
普遍萨克斯-不可摧毁的实数组合族
本文引入了实数组合族的算术类型的概念,用于推广组合集理论中常见的疯狂族、极大共有限群、超滤基、分裂族以及其他类似类型的族。然后,我们证明了每一个算术型实数组合族,如果它是由Sacks强迫S的乘积不能被破坏的,那么它实际上是普遍的Sacks-不可破坏的,即它是由任何长度的Sacks强迫的可数支持迭代或乘积不能被破坏的。进一步,在CH条件下,我们给出了各种算术类型族的普遍sacks -不可灭族的统一构造。特别地,我们证明了CH下一个普遍的sacks -不可破极大共群的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
12.50%
发文量
78
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.
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