Model-theoretic Characterizations of Large Cardinals
Logic
2019-03-19 v3
Abstract
We consider compactness characterizations of large cardinals. Based on results of Benda \cite{b-sccomp}, we study compactness for omitting types in various logics. In , this allows us to characterize any large cardinal defined in terms of normal ultrafilters, and we also analyze second-order and sort logic. In particular, we give a compactness for omitting types characterization of huge cardinals, which have consistency strength beyond Vop\v{e}nka's Principle.
Keywords
Cite
@article{arxiv.1708.07561,
title = {Model-theoretic Characterizations of Large Cardinals},
author = {Will Boney},
journal= {arXiv preprint arXiv:1708.07561},
year = {2019}
}