An Inconsistent Forcing Axiom at $\omega_2$
Stevo Todor\v{c}evi\'c, Shihao Xiong
TL;DR
This paper demonstrates the inconsistency of a specific forcing axiom related to certain posets at , establishing a new boundary for extending Martin's Axiom to .
Contribution
It introduces a new inconsistency result for a forcing axiom at , expanding the understanding of limitations in set-theoretic forcing.
Findings
The forcing axiom for countably compact, -Knaster, well-met posets is inconsistent.
This result builds on and complements Shelah's previous inconsistency findings.
It sets a new limit for generalizing Martin's Axiom to .
Abstract
We show that the forcing axiom for countably compact, -Knaster, well-met posets is inconsistent. This is supplemental to an inconsistency result of Shelah and sets a new limit to the generalization of Martin's Axiom to the stage of .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory