A Generalization of Martin's Axiom
David Asper\'o, Miguel Angel Mota
TL;DR
This paper introduces a new chain condition called the .5 chain condition and a corresponding forcing axiom that generalizes Martin's Axiom, leading to novel insights into club-guessing failures on .
Contribution
It defines the .5 chain condition and develops a generalized forcing axiom that impacts the understanding of club-guessing on .
Findings
Introduces the .5 chain condition.
Establishes a generalized forcing axiom.
Shows uniform failures of club-guessing on .
Abstract
We define the chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on that don't seem to have been considered in the literature before.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · Computability, Logic, AI Algorithms