Universality properties of forcing
Logic
2025-03-07 v2
Abstract
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories can be embedded into a model constructed by forcing. Our results rely on the model-theoretic properties of good ultrafilters, for which we provide a new existence proof on non-necessarily complete Boolean algebras.
Keywords
Cite
@article{arxiv.2310.11691,
title = {Universality properties of forcing},
author = {Francesco Parente and Matteo Viale},
journal= {arXiv preprint arXiv:2310.11691},
year = {2025}
}
Comments
16 pages