Weak square and stationary reflection

G. Fuchs, A. Rinot

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


It is well-known that the square principle □ λ entails the existence of a non-reflecting stationary subset of λ+, whereas the weak square principle □λ∗ does not. Here we show that if μcf(λ) < λ for all μ < λ, then □λ∗ entails the existence of a non-reflecting stationary subset of Ecf(λ)λ+in the forcing extension for adding a single Cohen subset of λ+. It follows that indestructible forms of simultaneous stationary reflection entail the failure of weak square. We demonstrate this by settling a question concerning the subcomplete forcing axiom (SCFA), proving that SCFA entails the failure of □λ∗ for every singular cardinal λ of countable cofinality.

Original languageEnglish
Pages (from-to)393-405
Number of pages13
JournalActa Mathematica Hungarica
Issue number2
StatePublished - 1 Aug 2018

Bibliographical note

Funding Information:
∗Corresponding author. †The first author was partially supported by PSC-CUNY grant 69656-00 47. ‡The second author was partially supported by the Israel Science Foundation 1630/14). Key words and phrases: weak square, simultaneous stationary reflection, SCFA. Mathematics Subject Classification: primary 03E35, secondary 03E57, 03E05.

Publisher Copyright:
© 2018, Akadémiai Kiadó, Budapest, Hungary.


  • SCFA
  • simultaneous stationary reflection
  • weak square


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