The Midwest Computability Seminar is a joint venture between the University of Chicago, the University of Notre Dame, the University of Wisconsin-Madison, and the University of Illinois Chicago. 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.

DATE: Tuesday, November 7th, 2023

PLACE: John Crerar Library Building 390, The University of Chicago.

5730 South Ellis Avenue, Chicago, IL 60637 (see maps.uchicago.edu).

REMOTE ATTENDANCE: https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09

Meeting ID: 997 5433 2165

Passcode: midwest

Speakers:

- Peter Cholak - University of Notre Dame

- David Gonzalez - University of California, Berkeley

- Tiago Royer - University of Chicago

- 12:00 - 1:00 The room will be available for a brown bag
lunch
- 1:00 - 1:50 Peter Cholak

- 2:00 - 2:30 Coffee Break
- 2:30 - 3:20 David Gonzalez

- 3:30 - 4:00 Coffee Break

- 4:00 - 4:50 Tiago Royer

- 5:30 Dinner TBA

Title: Some Computability Theoretic Aspects of Dobrinenâ€™s Result that the Universal Triangle Free Graph Has Finite Big Ramsey Degree

Abstract: We will discuss recent work of Cholak, Dobrinen, and McCoy. Mostly we will focus on colorings within the universal triangle free graph of nodes, edges, and non edges. The result that the universal triangle free graph has finite big Ramsey degree implies for colorings of nodes, edges, or non edges there is a copy of the universal triangle free graph with a minimal number of colors. The minimum depends on the objects we are coloring, not the coloring itself. We will discuss this number for our 3 cases. A copy of the universal triangle free graph with a minimal number of colors is called a minimal heterogeneous copy. We will also discuss what is known about the computability theoretic complexity of these minimal heterogeneous copies.

Title: The omega-Vaught's Conjecture

Abstract: Robert Vaught conjectured that the number of countable models of any given list of axioms must be either countable or continuum, but never in between. Despite all the work that has gone into this conjecture over the past sixty years, it remains open. It is one of the most well-known, long-standing open questions in mathematical logic. We introduce the omega-Vaught's conjecture, a strengthening of Vaught's conjecture for infinitary logic. We have shown this conjecture holds for linear orderings, a strengthening of Vaught's conjecture for linear orderings originally proved by Steel. The approach notably differs from Steel's proof (and any other previously known proof of Vaught's conjecture for linear orderings) in that it makes no appeal to lemmas from higher computability theory or descriptive set theory. This talk is based on joint work with Antonio Montalbán.

Title: Asymptotic Notions of Computability

Abstract: In the classical setting, we consider that a Turing machine solves a problem if, for all inputs, the machine halts with the correct output for this problem. We can relax this notion by requiring the machine to halt and be correct only on asymptotically all inputs. If we still require the machine to always halt, we have coarse computability; if we allow the machine to not halt sometimes but require it to always be correct when it does, we have generic computability. I will talk about these notions and their degree structures, and I will present a proof that there are minimal degrees for coarse reducibility.

- Sept 23rd 2008 Antonio Montalbán - Logan Axon - Joe Miller
- Nov 11th 2008 Chris Conidis - Keng Meng (Selwyn) Ng - Peter Gerdes
- Feb 3rd 2009 David Diamondstone - Bart Kastermans - Richard A. Shore
- April 21st 2009 Dan Turetsky - Julia Knight - Ted Slaman
- Sept 29th 2009 Carl Jockusch - Rachel Epstein - Rebecca Weber
- Jan 26th 2010 Sara Quinn - John Wallbaum - Steffen Lempp - Reed Solomon
- May 11th 2010 Adam Day - Liang Yu - Rod Downey - Boris Zilber
- Sept 28th 2010 Maurice Chiodo - Peter Gerdes - Damir Dzhafarov - Andy Lewis
- Feb 15th 2011 Uri Andrews - Paola D'Aquino - David Diamondstone - Christopher Porter - Rebecca Steiner
- Nov 1st 2011 Mingzhong Cai - Chris Conidis - Stephen Flood - Jeff Hirst - Asher Kach
- Nov 15th 2012 Achilles Beros - Rod Downey - Jesse Johnson - Sam Sanders - Steven VanDendriessche - Matthew Wright
- April 2nd 2013 Howard Becker - Denis Hirschfeldt - Paul Schupp
- October 1st 2013 Peter Cholak - Mushfeq Khan - Victor Ocasio-González - Jonathan Stephenson
- April 29th, 2014 Rod Downey - Noam Greenberg - Gregory Igusa - Alexander Melnikov - Kyle Riggs
- September 30th, 2014 Eric Astor - Quinn Culver - Jack Lutz - Timothy McNicholl
- February 17th, 2015 Carl Jockusch - Julia Knight - Steffen Lempp
- January 28th, 2016 Reese Johnston - Rutger Kuyper - Mariya Soskova - Mars Yamaleev
- October 22nd and 23rd, 2016 Special Meeting in Honor of Carl Jockusch's 75th Birthday
- March 16th, 2017 Greg Igusa - Jack Lutz - Sasha Melnikov - Reed Solomon
- October 24th, 2017 Noah Schweber - Don Stull - Dan Turetsky - Rose Weisshaar
- April 17th, 2018 Peter Cholak - Meng-Che "Turbo" Ho - Ethan McCarthy - Joe Miller
- October 9th, 2018 Uri Andrews - Timothy McNicholl - Alexandra Soskova
- April 18th, 2019 Wesley Calvert - Russell Miller - Steffen Lempp
- February 11th, 2020 Rachael Alvir - Tejas Bhojraj - Jun Le Goh - Neil Lutz
- August - December, 2020 Nine Online Talks
- February - May, 2021 Seven Online Talks
- September - December, 2021 Ten Online Talks
- January - April, 2022 Six Online Talks
- November 1st, 2022 Luca San Mauro - Donald Stull - Manlio Valenti
- May 2nd, 2023 Peter Gerdes - Joel David Hamkins - Matthew Harrison-Trainor

If you haven't been receiving the announcements and would like to be included in the list, send an email to drh@math.uchicago.edu.