Small $$\mathfrak {u}(\kappa )$$ u ( κ ) at singular $$\kappa $$ κ with compactness at $$\kappa ^{++}$$ κ + +

Archive for Mathematical Logic 61 (1):33-54 (2021)
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Abstract

We show that the tree property, stationary reflection and the failure of approachability at \ are consistent with \= \kappa ^+ < 2^\kappa \), where \ is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if \ is a regular cardinal, then stationary reflection at \ is indestructible under all \-cc forcings.

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References found in this work

Aronszajn trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Fragility and indestructibility of the tree property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
Indestructibility of the tree property.Radek Honzik & Šárka Stejskalová - 2020 - Journal of Symbolic Logic 85 (1):467-485.
The eightfold way.James Cummings, Sy-David Friedman, Menachem Magidor, Assaf Rinot & Dima Sinapova - 2018 - Journal of Symbolic Logic 83 (1):349-371.

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