Strongly unfoldable, splitting and bounding

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2023-05-24 DOI:10.1002/malq.202200003

Ömer Faruk Bağ, Vera Fischer

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引用次数: 0

Abstract

Assuming $GCH$ , we show that generalized eventually narrow sequences on a strongly inaccessible cardinal κ are preserved under a one step iteration of the Hechler forcing for adding a dominating κ-real. Moreover, we show that if κ is strongly unfoldable, $2^{κ} = κ^{+}$ and λ is a regular cardinal such that $κ^{+} < λ$ , then there is a set generic extension in which $s (κ) = κ^{+} < b (κ) = c (κ) = λ$ .

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强不可折叠、拆分和绑定

假设GCH$\mathsf{GCH}$，我们证明了在强不可访问基数κ上的广义最终窄序列在Hechler强迫的一步迭代下被保留，以添加支配κ-实数。此外，我们还证明了如果κ是强不可折叠的，2κ=κ+$2^\kappa=\kappa^+$并且λ是正则基数，使得κ+<；λ$\kappa^+<；\λ$，则存在s（κ）＝κ+<；b（κ）=c（κ）=λ$\mathfrak｛s｝（\kappa）=\kappa^+<；\mathfrak｛b｝（\kappa）=\mathfrak｛c｝（\ kappa。

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.