Strongly unfoldable, splitting and bounding

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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