# Sealing Kurepa Trees in ZFC

Seminar
Speaker
Itamar Giron (HUJI)
Date
24/11/2022 - 16:00 - 14:00Add to Calendar 2022-11-24 14:00:00 2022-11-24 16:00:00 Sealing Kurepa Trees in ZFC A class of trees may be defined using shared properties: height, width, cardinality of  the branch set, etc. For a tree T within a model M we ask if we may add a branch (or branches) to the model using some forcing notion without destroying said properties. If we cannot, we say the tree is sealed. A natural followup question is, under what conditions can we build a forcing notion which does not harm the properties of the tree, and seals it? In this lecture I show that given a Kurepa tree in M without any other assumptions on the model (except that it is a model of ZFC), we can construct a proper forcing-notion which forces a tree to be sealed for every forcing-notion from the ground model, without collapsing \aleph_2 and \aleph_1 . Building 505, room 62 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 505, room 62
Abstract

A class of trees may be defined using shared properties: height, width, cardinality of  the branch set, etc. For a tree T within a model M we ask if we may add a branch (or branches) to the model using some forcing notion without destroying said properties. If we cannot, we say the tree is sealed. A natural followup question is, under what conditions can we build a forcing notion which does not harm the properties of the tree, and seals it? In this lecture I show that given a Kurepa tree in M without any other assumptions on the model (except that it is a model of ZFC), we can construct a proper forcing-notion which forces a tree to be sealed for every forcing-notion from the ground model, without collapsing \aleph_2 and \aleph_1 .

תאריך עדכון אחרון : 15/11/2022