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 or has small consistency strength, but that of a cardinal 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.
Cite
@article{arxiv.2209.12144,
title = {Generically extendible cardinals},
author = {Toshimichi Usuba},
journal= {arXiv preprint arXiv:2209.12144},
year = {2024}
}