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arXiv · 2310.11691

Universality properties of forcing

Francesco Parente·Matteo Viale
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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.

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BibTeXRIS

Francesco Parente, Matteo Viale. 2023-10-18. Universality properties of forcing. https://doi.org/10.1017/jsl.2025.17

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