The Midwest Computability Seminar meets twice in the fall and twice in the spring at University of Chicago. Researchers in computability theory and their students and postdocs from University of Chicago, University of Notre Dame, and University of Wisconsin-Madison plus some others throughout the area regularly attend. Normally we have two half hour talks and two 1-hour talks and a few hours to talk and collaborate with each other. The seminar started in the fall of 2008.

DATE: Tuesday, September 28th, 2010.

PLACE: Ryerson, University of Chicago.

1100 East 58th Street, Chicago, IL 60637.

Speakers:

- Maurice Chiodo - University of Melbourne

- Peter Gerdes - U. of Notre Dame.

- Damir Dzhafarov - U. of Chicago.

- Andy Lewis - U. of Leeds.

- 12:00 - 1:00: Lunch. (the Barn Ry 352)
- 1:00 - 1:25: Maurice Chiodo
(the Barn Ry 352).

- 1:35 - 2:00: Peter Gerdes (the Barn Ry 352).
- 2:00 - 2:30: Coffee break

- 2:30 - 3:20: Damir Dzhafarov
(the Barn Ry 352).

- 3:30 - 4:10: Coffee break.
- 4:10 - 5:00: Andy Lewis (Eckhart
206).

- 6pm: Dinner. Mabenka Restarurant. 7844 S Cicero Ave. Burbank,
Illinois

Maurice Chiodo

Title: Enumerating subgroups,
and the computational complexity of recognising torsion-freeness, in
finitely presented groups.

Abstract: We give a
construction for a finitely presented group G for which the set of
finitely presented groups that embed into G is not recursively
enumerable. We do this by showing that from a description of a
recursively enumerable set A, we can uniformly construct a finitely
presented group G(A) such that the set of orders of torsion elements in
G(A) is one-one equivalent to A. As a corollary we show an earlier
result by Lempp that the set of torsion-free finitely presented groups
is Pi-0-2 complete in the Arithmetic Hierarchy.

Peter Gerdes

Title: A w-REA Set Forming A
Minimal Pair With 0'

Abstract: It is easy to see
that no n-REA set can form a (non-trivial) minimal pair with
0' and only slightly more difficult to observe that no w-REA set
can form a (non-trivial) minimal pair with 0''. Shore has asked
whether this can be improved to show that no w-REA set forms a
(non-trivial) minimal pair with 0'. We show that no such
improvement is possible by constructing a w-REA set C forming a minimal
pair with 0'.

Damir Dzhafarov

Title: Reverse mathematics and
equivalents of the axiom of choice.

Abstract: I will discuss recent
joint work with Carl Mummert studying the reverse mathematics of
various maximality principles classically equivalent to the axiom of
choice. We show that these principles have a wide range of
strengths in the context of second-order arithmetic, from being
equivalent to Z_2, to lying below ACA_0 and being incomparable with
WKL_0. Principles of the latter kind form a rich and complicated
structure. I will discuss some recent development in its study,
and how choice principles fit into it. For example, our results
show that modulo \Sigma^0_2 induction, the principle FIP, which asserts
that every family of nonempty sets has a maximal subfamily with the
property that any finite intersection of its members is nonempty, lies
strictly below the principle AMT studied by Hirschfeldt, Shore, and
Slaman [2009], and implies the principle OPT. This gives a
surprising connection between the reverse mathematical content of model
theoretic principles on the one hand, and of set-theoretic principles
on the other.

Andy Lewis

Title: The search for natural
definability in the Turing degrees

Abstract: While the
definability of all jump classes other than low has been established
through coding techniques, there remains a conspicuous lack of

any natural definability results in the Turing degrees -- I shall
detail the state of affairs in a program which looks to address this
issue by systematically analyzing the order theoretic properties
satisfied by the degrees in the various jump classes.

- Sept 23th 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 21th 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

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