Events - 2016

Tuesday, November 29, 2016 — 3:30 PM EST

Michael Deveau, Department of Pure Mathematics, University of Waterloo

Thursday, November 17, 2016 — 2:00 PM EST

**Please note change of time**

Michael Wan, University of California, Berkeley

Tuesday, November 15, 2016 — 3:30 PM EST

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

Tuesday, November 8, 2016 — 3:30 PM EST

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

Monday, October 31, 2016 — 2:30 PM EDT

Ross Willard, Department of Pure Mathematics, University of Waterloo

Tuesday, October 25, 2016 — 3:30 PM EDT

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

Thursday, October 20, 2016 — 2:30 PM EDT

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.

Tuesday, October 18, 2016 — 3:30 PM EDT

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

Friday, September 30, 2016 — 3:30 PM EDT

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

Thursday, September 29, 2016 — 2:30 PM EDT

Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo

Tuesday, September 27, 2016 — 3:30 PM EDT

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

This week we start chapter 2 and introduce some Relatively intrinsic notions. Basically we discuss R.i.c.e. (relatively intrinsic computably enumerable) relations and give some examples. Our goal is to prove a characterization theorem for R.i.c.e. relations.

MC 5417

Tuesday, September 20, 2016 — 3:30 PM EDT

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

Thursday, September 15, 2016 — 2:30 PM EDT

Omar Leon-Sanchez, McMaster University

Tuesday, September 13, 2016 — 3:30 PM EDT

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

Wednesday, July 27, 2016 — 10:00 AM EDT

Michael Deveau, Department of Pure Mathematics, University of Waterloo

 

At long last, we will show that the K-trivial set A we have been considering is low for K. To do this, we will expand on the brief teaser presented last time and show how a golden run may be augmented to build a request set W that witnesses that A is low for K. Of course, we have one final speed bump to take care of first: we must show that W is a bounded request set.

Wednesday, July 20, 2016 — 10:00 AM EDT

Michael Deveau, Department of Pure Mathematics, University of Waterloo

Wednesday, June 29, 2016 — 10:00 AM EDT

Michael Deveau, Department of Pure Mathematics, University of Waterloo

Wednesday, June 15, 2016 — 10:00 AM EDT

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

Last week we saw how to prove that a K-trivial real cannot be Turing complete, but we made several simplifying assumptions that set constants equal to zero.

This week, we will show how to modify the construction we used to make it work when the constants are allowed to take on arbitrary values.

MC 5403

Wednesday, June 8, 2016 — 10:00 AM EDT

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

 

Last week we introduced the decanter method, which we used to show that there is no wtt-complete K-trivial.

Wednesday, June 1, 2016 — 10:00 AM EDT

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

Wednesday, March 16, 2016 — 3:30 PM EDT

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

 

Last time we have seen an upper bound on the number of K-trivial sets via some constant b. This week we compute a lower bound which as we will see is also a ”tight” bound (close to the exact number).

MC 5403

Wednesday, March 9, 2016 — 3:30 PM EST

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

Wednesday, March 2, 2016 — 3:30 PM EST

Michael Deveau, Department of Pure Mathematics, University of Waterloo

We first discuss lowness for pairs of randomness notions, and then begin proving the theo- rem mentioned last time: Low(W2R,MLR) = Low(MLR).

MC 5403

Wednesday, February 10, 2016 — 3:30 PM EST

Michael Deveau, Department of Pure Mathematics, University of Waterloo

We briefly recall the definition of a base for ML-randomness presented last time. The remaining portion of the talk will be spent stating and proving an important result about such sets, namely that every base for ML-randomness is low for K.

MC 5403

Thursday, February 4, 2016 — 3:30 PM EST

Alex Kruckman, University of California, Berkeley

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