Generic selective independent families

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2026-02-15 Epub Date: 2025-07-04 DOI:10.1016/j.topol.2025.109504

Vera Fischer, Corey Bacal Switzer

引用次数: 0

Abstract

We prove that the generic maximal independent family obtained by iteratively forcing with the Mathias forcing relative to diagonalization filters is densely maximal. Moreover, by choosing the filters with some care one can ensure the family is selective and hence forcing indestructible in a strong sense. Using this we prove that under

p = 2^{ℵ_{0}}

there are selective independent families and also we show how to add selective independent families of any desired size.

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一般选择性独立家族

我们证明了用Mathias强迫相对于对角化滤波器的迭代强迫得到的一般极大独立族是密集极大的。此外，通过仔细选择过滤器，可以确保家庭是有选择性的，从而在强烈的意义上强迫坚不可摧。利用这一方法，我们证明了在p=2 ~ 0条件下存在选择性独立族，并展示了如何添加任意大小的选择性独立族。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.