Indestructibility of some compactness principles, part 1

Seminar
Speaker
Šárka Stejskalová (Institute of Mathematics, Prague)
Date
20/01/2020 - 15:00 - 13:00Add to Calendar 2020-01-20 13:00:00 2020-01-20 15:00:00 Indestructibility of some compactness principles, part 1 In the talk we will focus on compactness principles at the double successor of a regular cardinal kappa. We start by showing that if kappa^{<kappa} =kappa and lambda>kappa is a weakly compact cardinal, then in the Mitchell model V[M(kappa,lambda)] the tree property at kappa^{++} is indestructible under all kappa^+-cc forcing notions which live in the intermediate submodel V[Add(kappa,lambda)]. This result has direct applications for Prikry-style forcing notions and hence for the tree property at the double successor of a singular strong limit cardinal (it simplifies existing results and can be used to prove new results). Then we will discuss stationary reflection and its variants and the indestructibility under kappa^+-cc forcing notions. Area 502, Room 37 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Area 502, Room 37
Abstract

In the talk we will focus on compactness principles at the double successor of a regular cardinal kappa. We start by showing that if kappa^{<kappa} =kappa and lambda>kappa is a weakly compact cardinal, then in the Mitchell model V[M(kappa,lambda)] the tree property at kappa^{++} is indestructible under all kappa^+-cc forcing notions which live in the intermediate submodel V[Add(kappa,lambda)]. This result has direct applications for Prikry-style forcing notions and hence for the tree property at the double successor of a singular strong limit cardinal (it simplifies existing results and can be used to prove new results). Then we will discuss stationary reflection and its variants and the indestructibility under kappa^+-cc forcing notions.

Last Updated Date : 13/01/2020