当地的选择原则

Pub Date : 2022-05-07 DOI:10.1002/malq.202000089
Farmer Schlutzenberg
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引用次数: 2

摘要

假设ZFC $\mathsf {ZFC}$。设κ为基数。一个 & lt;κ ${\mathord {<}\hspace{1.111pt}\kappa}$ - ground是一个可传递的固有类W,它对ZFC $\mathsf {ZFC}$建模,使得V是W的一个泛型扩展,通过在W$的基数中强制P∈W$ \mathbb {P}\& lt;κ ${\mathord {<}\hspace{1.111pt}\kappa}$。κ-地幔M κ $\mathcal {M}_\kappa$是所有<κ ${\mathord {<}\hspace{1.111pt}\kappa}$ -grounds。我们证明了M κ $\mathcal {M}_\kappa$中的某些部分选择原理是κ不可及/弱紧致的结果,以及其他一些相关事实。
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Choice principles in local mantles

Assume ZFC $\mathsf {ZFC}$ . Let κ be a cardinal. A < κ ${\mathord {<}\hspace{1.111pt}\kappa }$ -ground is a transitive proper class W modelling ZFC $\mathsf {ZFC}$ such that V is a generic extension of W via a forcing P W $\mathbb {P}\in W$ of cardinality < κ ${\mathord {<}\hspace{1.111pt}\kappa }$ . The κ-mantle M κ $\mathcal {M}_\kappa$ is the intersection of all < κ ${\mathord {<}\hspace{1.111pt}\kappa }$ -grounds. We prove that certain partial choice principles in M κ $\mathcal {M}_\kappa$ are the consequence of κ being inaccessible/weakly compact, and some other related facts.

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