The Strength of Menger's Conjecture

DOI10.1016/J.TOPOL.2020.107536arXiv2006.16000WikidataQ113862548 ScholiaQ113862548MaRDI QIDQ6343976

Stevo Todorčević, S. Tokgoz, Franklin D. Tall

Publication date: 25 June 2020

Abstract: Menger conjectured that subsets of R with the Menger property must be

s i g m a

-compact. While this is false when there is no restriction on the subsets of R, for projective subsets it is known to follow from the Axiom of Projective Determinacy, which has considerable large cardinal consistency strength. We note that in fact, Menger's conjecture for projective sets has consistency strength of only an inaccessible cardinal.

Mathematics Subject Classification ID

Descriptive set theory (03E15) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Consistency and independence results in general topology (54A35)

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