Por Duarte Maia (University of Chicago).
In this talk, I will give a brief introduction to the areas of Computable Model Theory and Computable Structure Theory (which are close to each other, but distinct). I will introduce the so-called Slaman-Wehner Theorem, which roughly states that there is a countable graph G that encapsulates the property of being noncomputable, in the following sense: A Turing degree d can compute a copy of G iff d \neq 0. This theorem has historically been proven in three different ways, one due to Slaman, one due to Wehner, and more recently one based on results due to Hirschfeldt. We will sketch the proof based on Hirschfeldt's results and, time permitting, discuss related avenues of research.
I will assume basic knowledge of computability theory (Turing Reducibility, Church-Turing Thesis) and of first-order logic (Completeness Theorem, Henkin construction). I will mention some notions from model theory (atomic models, types), but they will be auxiliary and should not be required to understand the talk.
Transmissão via Zoom (pw: 919 4789 5133).
