Year: 2025
Type: article
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.
Source: Journal of Symbolic Logic
DOI: 10.1017/jsl.2025.17
Authors: FRANCESCO PARENTE, MATTEO VIALE
Institutions: Kobe University, University of Turin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408207657