Preservation of a Souslin tree and side conditions

2014/07/15 by Giorgio Venturi, Venturi, Giorgio
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #math.LO

paper · pdf · doi:10.48550/arxiv.1407.4050

arxiv created 2014/07/15 · openalex publication_date 2014/07/15 · arxiv updated 2014/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how to force, with finite conditions, the forcing axiom PFA(T), a relativization of PFA to proper forcing notions preserving a given Souslin tree T. The proof uses a Neeman style iteration with generalized side conditions consisting of models of two types, and a preservation theorem for such iterations. The consistency of this axiom was previously known by the standard countable support iteration, using a preservation theorem due to Miyamoto.

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