关于科恩和普里克里强迫观念

IF 0.5 3区数学 Q3 LOGIC

Journal of Symbolic Logic Pub Date : 2023-09-11 DOI:10.1017/jsl.2023.59

TOM BENHAMOU, MOTI GITIK

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引用次数: 7

摘要

摘要(1)我们证明了在$\kappa $上用Prikry强迫将$\kappa ^+$ -Cohen子集添加到$\kappa $是可能的。这回答了[9]中的一个问题。(2)介绍了非高尔文特性的强化方法。使用单一可测量基数证明是一致的，这改进了S. Garti, S. Shelah和第一作者[5]先前的结果。(3)研究了基于扩展器的Prikry强迫的情况。这与H.伍丁的一个问题有关。

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ON COHEN AND PRIKRY FORCING NOTIONS

Abstract (1) We show that it is possible to add $\kappa ^+$ -Cohen subsets to $\kappa $ with a Prikry forcing over $\kappa $ . This answers a question from [9]. (2) A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author [5]. (3) A situation with Extender-based Prikry forcings is examined. This relates to a question of H. Woodin.

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来源期刊

Journal of Symbolic Logic 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Symbolic Logic publishes research in mathematical logic and its applications of the highest quality. Papers are expected to exhibit innovation and not merely be minor variations on established work. They should also be of interest to a broad audience. JSL has been, since its establishment in 1936, the leading journal in the world devoted to mathematical logic. Its prestige derives from its longevity and from the standard of submissions -- which, combined with the standards of reviewing, all contribute to the fact that it receives more citations than any other journal in logic.