The $κ$-Strongly Proper Forcing Axiom
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866910369273872384 |
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| author | Asperó, David Cox, Sean Karagila, Asaf Weiss, Christoph |
| author_facet | Asperó, David Cox, Sean Karagila, Asaf Weiss, Christoph |
| contents | We study methods to obtain the consistency of forcing axioms, and particularly higher forcing axioms. We first force over a model with a supercompact cardinal $θ>κ$ to get the consistency of the forcing axiom for $κ$-strongly proper forcing notions which are also $κ$-lattice, and then eliminate the need for large cardinals. The proof goes through a natural reflection property for $κ$-strongly proper forcings. We also produce a model of this forcing axiom with $2^κ$ arbitrarily large, and prove the inconsistency of certain natural strengthenings of the axiom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_02130 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The $κ$-Strongly Proper Forcing Axiom Asperó, David Cox, Sean Karagila, Asaf Weiss, Christoph Logic Primary 03E57, Secondary 03E55, 03E35 We study methods to obtain the consistency of forcing axioms, and particularly higher forcing axioms. We first force over a model with a supercompact cardinal $θ>κ$ to get the consistency of the forcing axiom for $κ$-strongly proper forcing notions which are also $κ$-lattice, and then eliminate the need for large cardinals. The proof goes through a natural reflection property for $κ$-strongly proper forcings. We also produce a model of this forcing axiom with $2^κ$ arbitrarily large, and prove the inconsistency of certain natural strengthenings of the axiom. |
| title | The $κ$-Strongly Proper Forcing Axiom |
| topic | Logic Primary 03E57, Secondary 03E55, 03E35 |
| url | https://arxiv.org/abs/1912.02130 |