Mathias and silver forcing parametrized by density

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2023-05-18 DOI:10.1007/s00153-023-00881-7

Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle

引用次数: 1

Abstract

We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse \(2^\omega \) to \(\omega \), while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.

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Mathias和silver力的密度参数化

我们从低密度和高密度的角度定义和研究了Silver和Mathias作用力的不同版本。重点讨论了性质、公理A、链条件、基数的保存和Cohen实数的添加。我们发现粗糙的外力会坍塌\(2^\omega \)到\(\omega \)，而其他外力则会出奇地温和。我们还研究了由这些参数化强迫概念引起的正则性与Baire性质之间的联系。

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

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.