The strength of Menger's conjecture

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Tall F. D., Todorcevic S., TOKGÖZ S.

TOPOLOGY AND ITS APPLICATIONS, cilt.301, 2021 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 301
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.topol.2020.107536
  • Dergi Adı: TOPOLOGY AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Menger, Hurewicz, sigma-compact, Co-analytic, Projective set of reals, L(R), Hurewicz Dichotomy, SPACES, HUREWICZ, SET
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.