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A small ultrafilter number at smaller cardinals
Archive for Mathematical Logic 59 (3-4):325-334 (2020)
Abstract
It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on \ which is generated by fewer than \ sets.Other Versions
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Citations of this work
Small $$\mathfrak {u}(\kappa )$$ u ( κ ) at singular $$\kappa $$ κ with compactness at $$\kappa ^{++}$$ κ + +.Radek Honzik & Šárka Stejskalová - 2021 - Archive for Mathematical Logic 61 (1):33-54.
On configurations concerning cardinal characteristics at regular cardinals.Omer Ben-Neria & Shimon Garti - 2020 - Journal of Symbolic Logic 85 (2):691-708.
References found in this work
Iterated perfect-set forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
The weak □* is really weaker than the full □.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029 - 1033.
Set Theory: On the Structure of the Real Line.T. Bartoszyński & H. Judah - 1999 - Studia Logica 62 (3):444-445.
Two Upper Bounds on Consistency Strength of $negsquare{aleph{omega}}$ and Stationary Set Reflection at Two Successive $aleph_{n}$.Martin Zeman - 2017 - Notre Dame Journal of Formal Logic 58 (3):409-432.
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