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) \(\kappa^+ = \mathfrak{t}(\kappa) < \mathfrak{u}(\kappa) < 2^\kappa\), 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 \(\kappa^+ < \mathfrak{t}(\kappa) \le \mathfrak{u}(\kappa) < 2^\kappa\) 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++
12.10.2023 16:45 - 17:30
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KGRC
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