Invariant Ideal Axiom

2022/04/06 by Michael Hrušák, Hrušák, Michael, Alexander Shibakov +1 · 1 citation
Mathematics · #03C20 #03E05 #03E35 #22A05 #54H11 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO #msc:03C20 #msc:03E05 #msc:03E35 #msc:22A05 #msc:54H11

paper · pdf · doi:10.48550/arxiv.2204.03079

arxiv created 2022/04/06 · arxiv updated 2022/04/08

Abstract

We introduce and prove the consistency of a new set theoretic axiom we call the Invariant Ideal Axiom. The axiom enables us to provide (consistently) a full topological classification of countable sequential groups, as well as fully characterize the behavior of their finite products. We also construct examples that demonstrate the optimality of the conditions in \IIA, and list a number of open questions.

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