An equiconsistency result on partial squares

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Journal of Mathematical Logic 11 (1):29-59 (2011)
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Abstract

We prove that the following two statements are equiconsistent: there exists a greatly Mahlo cardinal; there exists a regular uncountable cardinal κ such that no stationary subset of κ+ ∩ cof carries a partial square.

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10.1142/s0219061311000992

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Citations of this work

Knaster and friends II: The C-sequence number.Chris Lambie-Hanson & Assaf Rinot - 2020 - Journal of Mathematical Logic 21 (1):2150002.
Separating weak partial square principles.John Krueger & Ernest Schimmerling - 2014 - Annals of Pure and Applied Logic 165 (2):609-619.
In memoriam: James Earl Baumgartner (1943–2011).J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7):877-909.
Successive cardinals with no partial square.John Krueger - 2014 - Archive for Mathematical Logic 53 (1-2):11-21.

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References found in this work

Set theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
Reflecting stationary sets and successors of singular cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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