STATIONARY REFLECTION and the FAILURE of the SCH

Omer Ben-Neria, Yair Hayut, Spencer Unger

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and every collection of fewer than stationary subsets of reflects simultaneously. For >, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.

Original languageAmerican English
Pages (from-to)1-26
Number of pages26
JournalJournal of Symbolic Logic
Volume89
Issue number1
DOIs
StatePublished - 27 Mar 2024

Bibliographical note

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

Keywords

  • Prikry forcing
  • SCH.
  • stationary reflection

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