Forcing with matrices of countable elementary submodels
Seminar
Speaker
Roy Shalev (BIU)
Date
09/08/2022 - 13:00 - 11:00Add to Calendar
2022-08-09 11:00:00
2022-08-09 13:00:00
Forcing with matrices of countable elementary submodels
We present a forcing poset by Kuzeljevic and Todorcevic {https://www.ams.org/journals/proc/2017-145-05/S0002-9939-2017-13133-5/home.html}.
The conditions are finite matrices whose rows consist of isomorphic countable elementary submodels of a given structure of the form H_theta.
We will show that this forcing poset adds a Kurepa tree.
Moreover, forcing with a "continuous" modification adds an almost Souslin Kurepa tree, i.e., the level set of any antichain in the tree is not stationary in omega_1.
Seminar room
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
Seminar room
Abstract
We present a forcing poset by Kuzeljevic and Todorcevic {https://www.ams.org/journals/proc/2017-145-05/S0002-9939-2017-13133-5/home.html}.
The conditions are finite matrices whose rows consist of isomorphic countable elementary submodels of a given structure of the form H_theta.
We will show that this forcing poset adds a Kurepa tree.
Moreover, forcing with a "continuous" modification adds an almost Souslin Kurepa tree, i.e., the level set of any antichain in the tree is not stationary in omega_1.
Last Updated Date : 04/08/2022
