Club-guessing, stationary reflection, and coloring theorems
Todd Eisworth
TL;DR
This paper explores the connection between stationary reflection failures and strong coloring theorems at successors of singular cardinals, introducing new results in club-guessing and ideal theory.
Contribution
It establishes novel links between stationary set reflection failures and coloring theorems, advancing the understanding of club-guessing and ideal structures.
Findings
Strong coloring theorems derived from stationary reflection failures
New results in club-guessing theory
Advancements in the theory of ideals
Abstract
We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of ideals.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Computability, Logic, AI Algorithms