Choice principles in local mantles

Pub Date : 2022-05-07 DOI:10.1002/malq.202000089

Farmer Schlutzenberg

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引用次数: 2

Abstract

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

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当地的选择原则

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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