The κ-Strongly Proper Forcing Axiom

2019/12/04 by David Asperó, Asperó, David, Cox, Sean +2
Computer Science · Mathematics · #03E35 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Primary 03E57 #Secondary 03E55

paper · pdf · doi:10.48550/arxiv.1912.02130

openalex publication_date 2019/12/04 · openalex created_date 2019/12/13 · openalex updated_date 2026/07/28

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 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.

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