Critical Cardinals

Yair Hayut; Asaf Karagila

doi:10.1007/s11856-020-1998-8

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arXiv · 1805.02533

Critical Cardinals

Yair Hayut·Asaf Karagila

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Abstract

We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equivalent to measurability, but it is well-known that choice is necessary for the equivalence. Oddly enough, this central notion was never investigated on its own before. We prove a technical criterion for lifting elementary embeddings to symmetric extensions, and we use this to show that it is consistent relative to a supercompact cardinal that there is a critical cardinal whose successor is singular.

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BibTeX RIS

Yair Hayut, Asaf Karagila. 2019-05-29. Critical Cardinals. https://doi.org/10.1007/s11856-020-1998-8

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