Thu, 13 May 2021
16:30
16:30
Virtual
Applications of generalized indiscernible sequences
Lynn Scow
(California State University San Bernardino)
Abstract
We survey some of the applications of generalized indiscernible sequences, both in model theory and in structural Ramsey theory. Given structures $A$ and $B$, a semi-retraction is a pair of quantifier-free type respecting maps $f: A \rightarrow B$ and $g: B \rightarrow A$ such that $g \circ f: A \rightarrow A$ is quantifier-free type preserving, i.e. an embedding. In the case that $A$ and $B$ are locally finite ordered structures, if $A$ is a semi-retraction of $B$ and the age of $B$ has the Ramsey property, then the age of $A$ has the Ramsey property.