Archive for Mathematical Logic 61 (1):33-54 (2022)

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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DOI 10.1007/s00153-021-00776-5
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References found in this work BETA

Reflecting Stationary Sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Aronszajn Trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
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.
A small ultrafilter number at smaller cardinals.Dilip Raghavan & Saharon Shelah - 2020 - Archive for Mathematical Logic 59 (3-4):325-334.

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