The strength of Menger's conjecture

Creative Commons License

Tall F. D., Todorcevic S., TOKGÖZ S.

TOPOLOGY AND ITS APPLICATIONS, vol.301, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 301
  • Publication Date: 2021
  • Doi Number: 10.1016/j.topol.2020.107536
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: Menger, Hurewicz, sigma-compact, Co-analytic, Projective set of reals, L(R), Hurewicz Dichotomy, SPACES, HUREWICZ, SET
  • Hacettepe University Affiliated: Yes


Menger conjectured that subsets of R with the Menger property must be Sigma-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. (C) 2020 Elsevier B.V. All rights reserved.