Tree property at the first and double successors with arbitrary gaps, part 1

יום ב', 27/05/2019 - 13:00
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In this talk we shall present a proof of the consistency, modulo suitable large cardinals assumptions, of the following theory:
"There is a strong limit cardinal \kappa with cof(\kappa)>\aleph_0 such that TP(\kappa^+) and TP(\kappa^{++}) hold and 2^\kappa is arbitrarily large"
Here by arbitrarily large we mean that 2^\kappa can be any cardinal \gamma\geq \kappa^{++} with cof(\gamma)>\kappa.The proof relies on ideas of Sinapova, Unger and Friedman-Honzik-Stejskalová and provides a generalization to two results of Sinapova and Friedman-Honzik-Stejskalová, respectively.