We will use a construction due to Brooke-Taylor, Fischer, Friedman, and Montoya and construct a model where kappa is inaccessible and we have (among other things) kappa+ = t(kappa) < u(kappa) <
2^kappa, and the tree property, and the negation of the weak Kurepa Hypothesis hold at kappa++. This is an application of a general method based on indestructibility of various compactness principles by further forcings. The consistency of kappa+ < t(kappa) \le u(kappa) < 2^kappa with the same compactness principles remains open because it is not solved by the present technique.
The tower number and the ultrafilter number on an inaccessible cardinal kappa with compactness at kappa++
12.10.2013 16:45 - 12.10.2023 18:15
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KGRC
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