Clovis Hamel: Stability and Definability in Continuous Logics, Cp-theory and the Tsirelson space.

Place: Fields Institute Library
Date: Decembver 7, 2018 (13:30-15:00)
Speaker: Clovis Hamel
Title: Stability and Definability in Continuous Logics, Cp-theory and the Tsirelson space.
Abstract: An old question in Functional Analysis inquired whether there is a Banach space that
does not contain a copy of either lp or c0. Tsirelson defined such a space through
an infinitary process that inspired many other constructions of pathological spaces.
Then Gowers popularized the problem: does every explicitly definable infinite
dimensional Banach space contain a copy of lp or c0?
In first-order logic, the notion of explicit definability is closely related to that
of stability, which has been a driving force of Model Theory in the last decades
since Shelah introduced the idea. We will discuss how these concepts extend to
continuous logics in order to present Casazza and Iovino’s positive answer to
Gowers’s question in finitary continuous logic and our current work around this
result in infinitary continuous logics using Cp-theoretic tools.

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