共分析超滤碱

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2021-11-03 DOI:10.1007/s00153-021-00801-7

Jonathan Schilhan

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引用次数: 7

摘要

在描述集理论的意义上，基于\(\omega \)研究了超滤的可定义性。主要结果表明Ramsey超滤不存在共解析基，而在L中我们可以构造\(\Pi ^1_1\) p点和q点基。对于\(n \in \omega \)，我们还证明了\({\varvec{\Delta }}^1_{n+1}\)超滤基的存在与\({\varvec{\Pi }}^1_n\)超滤基的存在是等价的。此外，我们还引入了经典超滤数的Borel版本，并做了一些观察。

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Coanalytic ultrafilter bases

We study the definability of ultrafilter bases on \(\omega \) in the sense of descriptive set theory. As a main result we show that there is no coanalytic base for a Ramsey ultrafilter, while in L we can construct \(\Pi ^1_1\) P-point and Q-point bases. We also show that the existence of a \({\varvec{\Delta }}^1_{n+1}\) ultrafilter is equivalent to that of a \({\varvec{\Pi }}^1_n\) ultrafilter base, for \(n \in \omega \). Moreover we introduce a Borel version of the classical ultrafilter number and make some observations.

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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.