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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29521 |
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| _version_ | 1866908924902375424 |
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| author | Holy, Peter Palmer, Emma Schilhan, Jonathan |
| author_facet | Holy, Peter Palmer, Emma Schilhan, Jonathan |
| contents | We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present sufficient conditions for the preservation of the axioms of Gödel-Bernays set theory (without the axiom of choice), and for the forcing theorem to hold for class-sized symmetric systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A General Theory of Class Symmetric Systems Holy, Peter Palmer, Emma Schilhan, Jonathan Logic 03E25, 03E70 We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present sufficient conditions for the preservation of the axioms of Gödel-Bernays set theory (without the axiom of choice), and for the forcing theorem to hold for class-sized symmetric systems. |
| title | A General Theory of Class Symmetric Systems |
| topic | Logic 03E25, 03E70 |
| url | https://arxiv.org/abs/2603.29521 |