Adding highly generic subsets of ω 2 $\omega _2$

Pub Date : 2024-05-27 DOI:10.1002/malq.202300007

Rouholah Hoseini Naveh, Mohammed Golshani, Esfandiar Eslami

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Abstract

Starting from the generalized continuum hypothesis ( $GCH$ ), we build a cardinal and $GCH$ preserving generic extension of the universe, in which there exists a set $A \subseteq ω_{2}$ of size $ℵ_{2}$ so that every countably infinite subset of $A$ or $ω_{2} ∖ A$ is Cohen generic over the ground model.

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添加ω2$\omega _2$的高度通用子集

从广义连续统假设（）出发，我们建立了一个宇宙的有心和保全泛函扩展，其中存在一个大小为的集合，使得或的每一个可数无限子集都是地面模型上的科恩泛函。

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