Different covering numbers of compact tree ideals

IF 0.4 4区数学 Q4 LOGIC

Archive for Mathematical Logic Pub Date : 2024-08-16 DOI:10.1007/s00153-024-00933-6

Jelle Mathis Kuiper, Otmar Spinas

引用次数: 0

Abstract

We investigate the covering numbers of some ideals on \({^{\omega }}{2}{}\) associated with tree forcings. We prove that the covering of the Sacks ideal remains small in the Silver and uniform Sacks model, respectively, and that the coverings of the uniform Sacks ideal and the Mycielski ideal, \({\mathfrak {C}_{2}}\), remain small in the Sacks model.

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紧凑树理想的不同覆盖数

我们研究了 \({^{\omega }}{2}{}\) 上与树强制相关的一些理想的覆盖数。我们分别证明了萨克斯理想的覆盖数在 Silver 模型和统一萨克斯模型中仍然很小，并且证明了统一萨克斯理想和 Mycielski 理想、\({\mathfrak {C}_{2}}\) 的覆盖数在萨克斯模型中仍然很小。

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 数学-数学

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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.