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arXiv · 1912.02130

The $\kappa$-Strongly Proper Forcing Axiom

David Asperó·Sean Cox·Asaf Karagila·Christoph Weiss
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Abstract

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 $\theta>\kappa$ to get the consistency of the forcing axiom for $\kappa$-strongly proper forcing notions which are also $\kappa$-lattice, and then eliminate the need for large cardinals. The proof goes through a natural reflection property for $\kappa$-strongly proper forcings. We also produce a model of this forcing axiom with $2^\kappa$ arbitrarily large, and prove the inconsistency of certain natural strengthenings of the axiom.

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David Asperó, Sean Cox, Asaf Karagila, Christoph Weiss. 2019-12-04. The $\kappa$-Strongly Proper Forcing Axiom. https://arxiv.org/abs/1912.02130

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