36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"Partition theorems for uncountable expanded trees"

Shelah, Saharon

We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on subtrees of $ {}^{ \kappa g}2 $ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding to preserve the height of the tree. We get consistency results without large cardinals. On background see for example Dobrinen-Shelah. The intention is to apply it to model theoretic problems.

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