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Nick Ramsey : Invariants Related to the Tree Property

Posted by Kostyantyn Slutskyy , part of the Logic Seminar.

At
April 28, 2015, 4 p.m.
In
SEO 427
Abstract
A remarkable theorem of Shelah asserts that an unsimple theory is unsimple in one of two ways: either it has the tree property of the first kind or the tree property of the second kind. Artem Chernikov and I recently studied some possible `quantitative refinements' of this theorem, by considering the relations that obtain between several invariants related to the tree property introduced by Shelah in Chapter 3 of Classification Theory. I'll report on this work, as well as some more recent developments involving Shelah's theory of strong colorings.