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