控制后继基数上正常度量的数量

Pub Date : 2022-04-28 DOI:10.1002/malq.202000087

Arthur W. Apter

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引用次数: 0

摘要

我们研究了在选择公理为假的宇宙中，后继基数所能携带的正常测度的数目。当考虑奇异基数的后继时，我们建立了假设超紧性实例的相对一致性结果，以及超功率公理UA $\mathsf {UA}$(由Goldberg在[12]中引入)。当考虑正则基数的后继时，我们仅假设存在一个可测量基数，就建立了相对一致性结果。这允许一致性。

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Controlling the number of normal measures at successor cardinals

We examine the number of normal measures a successor cardinal can carry, in universes in which the Axiom of Choice is false. When considering successors of singular cardinals, we establish relative consistency results assuming instances of supercompactness, together with the Ultrapower Axiom $UA$ (introduced by Goldberg in [12]). When considering successors of regular cardinals, we establish relative consistency results only assuming the existence of one measurable cardinal. This allows for equiconsistencies.

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