Universality properties of forcing
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915183432040448 |
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| author | Parente, Francesco Viale, Matteo |
| author_facet | Parente, Francesco Viale, Matteo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11691 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universality properties of forcing Parente, Francesco Viale, Matteo Logic 03E40 (Primary) 03C50, 03E05 (Secondary) 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. |
| title | Universality properties of forcing |
| topic | Logic 03E40 (Primary) 03C50, 03E05 (Secondary) |
| url | https://arxiv.org/abs/2310.11691 |