Critical Cardinals

Por • 23 may, 2018 • Sección: Ambiente

Yair Hayut, Asaf Karagila

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.

arXiv:1805.02533v1 [math.LO] for this versión)

Logic (math.LO)

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