To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

For many (but not all) properties, a reduct of a structure M is no more complicated than M itself.  For example, if M is decidable, so are each of its reducts (in a reasonable language).  However, Borel completeness, which is a measure of ‘maximal complexity’ is not like this.  We recently showed that if M has uncountably many 1-types (with respect to its theory) then M has a Borel complete reduct.  No background is assumed -- at least the first half of the talk will be spent on defining reducts and Borel completeness, and giving algebraic examples.   This is joint work with Douglas Ulrich.