Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo
Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
R.i.c.e. relations can be characterized in a purely syntactic way using computably infinitary formulas and without referring to the different copies of the structure. We go through the proof of Theorem II.1.14 that establishes this characterization.
MC 5417
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
We will describe a way to interpret certain r.i.c.e relations as coding sets of natural numbers into structures. Using enumeration reductions, we will give a characterization of the sets of natural numbers which are coded in a structure in terms of the types of the tuples in that structure.
MC 5417
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
This seminar will discuss some of the ideas of computable structure theory, which aims to apply computability-theoretic ideas to structures from other areas of mathematics.
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
We will show that there is a natural way to form both finite and infinite joins of subsets of a structure. We will also introduce r.i.c.e complete relations, and show that every structure has a r.i.c.e. complete relation. We will use this to define a jump operator on relations in structures.
MC 5417
Ross Willard, Department of Pure Mathematics, University of Waterloo
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
We will show that the adjacency relation is structurally complete in linear orders, by expressing rice relations in terms of universal sentences over it.
MC 5417
**Please note change of time**
Michael Wan, University of California, Berkeley
Michael Deveau, Department of Pure Mathematics, University of Waterloo