English

Generically extendible cardinals

Logic 2024-11-26 v5

Abstract

In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of ω1\omega_1 or ω2\omega_2 has small consistency strength, but that of a cardinal >ω2>\omega_2 does not. We also consider some results concerned with generically extendible cardinals, such as indestructibility, generic absoluteness of the reals, and Boolean valued second order logic.

Keywords

Cite

@article{arxiv.2209.12144,
  title  = {Generically extendible cardinals},
  author = {Toshimichi Usuba},
  journal= {arXiv preprint arXiv:2209.12144},
  year   = {2024}
}
R2 v1 2026-06-28T02:02:16.203Z