Events

Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo

If $\mathcal{A}$ and $\mathcal{B}$ are two computable copies of a structure, their isomorphism spectrum is the set of Turing degrees that compute an isomorphism from $\mathcal{A}$ to $\mathcal{B}$. We introduce a framework for constructing computable structures with the property that the isomorphisms between arbitrary computable copies of these structures are constructed from isomorphisms between computable copies of their component structures. We call these \emph{computably composite structures}. We show that given any uniformly computable collection of isomorphism spectra, there exists a pair of computably composite structures whose isomorphism spectrum is the union of the original isomorphism spectra. We use this to construct examples of isomorphism spectra that are not equal to the upward closure of any finite set of Turing degrees.

MC 5479

Christoph Kesting, McMaster University

James Freitag showed that the Klein j-function is not pfaffian over the complex numbers. In this talk, I will give a brief introduction to pfaffian functions, their current place in model theory and Freitag's result. Then I will discuss recent work expanding Freitag's result to a restriction of the j-function to the imaginary interval (0, i) not being pfaffian over the real exponential field.

MC 5479

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

I will report on ongoing work with Moshe Kamensky toward developing a theory of binding groups for quantifier-free types in ACFA, well-suited for applications to rational algebraic dynamics.

MC 5479

Franklin Tall, University of Toronto

We show that Morley’s theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, large cardinals, and Inner Model Theory.

MC 5479