English

Reflection principles, generic large cardinals, and the Continuum Problem

Logic 2020-09-08 v2

Abstract

Strong reflection principles with the reflection cardinal 1\leq\aleph_1 or <20<2^{\aleph_0} imply that the size of the continuum is either 1\aleph_1 or 2\aleph_2 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.

Keywords

Cite

@article{arxiv.2009.01609,
  title  = {Reflection principles, generic large cardinals, and the Continuum Problem},
  author = {Sakaé Fuchino and André Ottenbreit Maschio Rodrigues},
  journal= {arXiv preprint arXiv:2009.01609},
  year   = {2020}
}
R2 v1 2026-06-23T18:17:30.818Z