# Tree property at the first and double successors with arbitrary gaps, part 3

Seminar
Speaker
Alejandro Poveda (Universitat de Barcelona)
Date
17/06/2019 - 15:00 - 13:00Add to Calendar 2019-06-17 13:00:00 2019-06-17 15:00:00 Tree property at the first and double successors with arbitrary gaps, part 3 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. Building 105, Room 61 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 105, Room 61
Abstract
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.

תאריך עדכון אחרון : 12/06/2019