Reflection principles, generic large cardinals, and the Continuum Problem

2020/09/03 by Fuchino, Sakaé, Rodrigues, André Ottenbreit Maschio · 1 citation
#03E50 #03E55 #03E65 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2009.01609

Abstract

Strong reflection principles with the reflection cardinal ≤ℵ₁ or <2^ℵ₀ imply that the size of the continuum is either ℵ₁ or ℵ₂ or very large. Thus, the stipulation, that a strong reflection principle should hold, seems to support the trichotomy on the possible size of the continuum. In this article, we examine the situation with the reflection principles and related notions of generic large cardinals.

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