A forcing axiom for a non-special Aronszajn tree

2018/05/21 by Krueger, John · 4 citations
#03E35 #03E57 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1805.08164

Abstract

Suppose that T^* is an ω₁-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA(T^*) for proper forcings which preserve these properties of T^*. We prove that PFA(T^*) implies many of the strong consequences of PFA, such as the failure of very weak club guessing, that all of the cardinal characteristics of the continuum are greater than ω₁, and the P-ideal dichotomy. On the other hand, PFA(T^*) implies some of the consequences of diamond principles, such as the existence of Knaster forcings which are not stationarily Knaster.

Cited by

• Entangled Suslin lines and OGA
• New consequences of PFA(T^*)
• Forcing Axioms and construction schemes
• Uniformization of ladder system colorings and stationary precaliber forcings

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