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MENAS’S CONJECTURE REVISITED

Part of: Set theory

Published online by Cambridge University Press:  08 May 2023

PIERRE MATET
PIERRE MATET*
Affiliation:
LLABORATOIRE DE MATHÉMATIQUES UNIVERSITÉ DE CAEN—CNRS BP 5186 14032 CAEN CEDEX, FRANCE E-mail: pierre.matet@unicaen.fr
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Abstract

In an article published in 1974, Menas conjectured that any stationary subset of can be split in many pairwise disjoint stationary subsets. Even though the conjecture was shown long ago by Baumgartner and Taylor to be consistently false, it is still haunting papers on . In which situations does it hold? How much of it can be proven in ZFC? We start with an abridged history of the conjecture, then we formulate a new version of it, and finally we keep weakening this new assertion until, building on the work of Usuba, we hit something we can prove.

Keywords

Menas’s conjectureideal on Pκ(λ)weak saturation

MSC classification

Primary: 03E05: Other combinatorial set theory
Secondary: 03E04: Ordered sets and their cofinalities; pcf theory

Information

Type
Articles
Information
Bulletin of Symbolic Logic , Volume 29 , Issue 3 , September 2023 , pp. 354 - 405
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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