Midwest Computability Seminar

Midwest Computability Seminar


The Midwest Computability Seminar is a joint venture between the University of Chicago, the University of Notre Dame, and the University of Wisconsin-Madison. It meets once or twice per semester at the University of Chicago, and is attended by faculty and students from these universities and others in the area. The seminar started in the fall of 2008.

VIDEOS:     Gerdes    Hamkins    Harrison-Trainor    (Panopto)    Gerdes    Hamkins    Harrison-Trainor    (YouTube)

SLIDES:     Gerdes    Hamkins    Harrison-Trainor

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(See https://goforward.uchicago.edu/.)

DATE: Tuesday, May 2nd, 2023

PLACE: Ryerson Hall 352 (the Barn), The University of Chicago.
1100 East 58th Street, Chicago, IL 60637.

REMOTE ATTENDANCE: https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09
Meeting ID: 997 5433 2165
Passcode: midwest




Peter Gerdes

Title: A non-trivial 3-REA set not computing a 3-generic

Abstract: It's well known that every non-computable r.e. set computes a 1-generic. In this talk I review this result, discuss the generalization to 2-REA sets and, if time permits, discuss a new result that there is a 3-REA set not computable from 0'' that doesn't compute a weak 3-generic.

Joel David Hamkins

Title: Set-theoretic forcing as a computational process

Abstract: I shall explore several senses in which set-theoretic forcing can be seen as a computational process on the models of set theory. Given an oracle for the atomic or elementary diagram of a model (M,∈M) of set theory, for example, there are senses in which one may compute M-generic filters G ⊂ ℙ ∈M over that model and compute the diagrams of the corresponding forcing extensions M[G]. Meanwhile, no such computational process is functorial, for there must always be isomorphic alternative presentations of the same model of set theory that lead by the computational process to non-isomorphic forcing extensions. Indeed, there is no Borel function providing generic filters that is functorial in this sense. This is joint work with myself, Russell Miller and Kameryn Williams.

Matthew Harrison-Trainor

Title: True stages and descriptive set theory

Abstract: I will explain how true stage constructions from computability theory can be used to prove strong change-of-topology results in descriptive set theory. A classical tool of descriptive set theory is to take a countable collection of Borel sets (often the sets of a particular lightface Borel complexity) and change the topology to make them open. Using the true stage machinery, we can create a tree (analagous to the trees of finite sequences for the usual topologies on Baire space and Cantor space) such that the closed sets of the new topology correspond to the sets of paths through a subtree. I will explain how this is done together with some applications. This is joint work with Adam Day, Noam Greenberg, and Dan Turetsky.

Previous Seminars:

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