Midwest
Computability Seminar
X
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 WisconsinMadison plus some others
throughout the area regularly attend. Normally we have half hour
talks and 1hour talks, though this varies, and a few hours to talk
and collaborate with each other. The seminar started in the
fall of 2008.
DATE: Tuesday, November 1, 2011.
PLACE: Ryerson, University of
Chicago.
1100 East 58th Street, Chicago, IL 60637.
Speakers:

Mingzhong
Cai  U. of Wisconsin.
 Chris Conidis  U. of Waterloo.
 Stephen Flood  U. of Notre Dame.
 Jeff Hirst  Appalachian State U.
 Asher Kach  U. of Chicago.
Schedule:
 12:00  1:00: Lunch. (the Barn Ry 352)
 1:05  1:30: Jeff Hirst.
 1:35  2:00: Stephen Flood.
 2:20  3:00: Mingzhong Cai.
 3:00  3:30:
Coffee break  Move to Eckhart 206 at 3:30.
 3:40 4:20: Asher Kach.
 4:35  5:15: Chris Conidis.
 6:00: Dinner  Lao Shanghai Restaurant.
2163
South China Place, Chicago, IL
Abstracts:
Speaker: Mingzhong Cai
Title: Definability problem
of domination properties
Abstract: We discuss the
definability problem for hyperimmunity and array nonrecursiveness.
Both notions are defined from domination notions regarding the rates
of growth of functions recursive in a degree. A positive result is
that array nonrecursiveness can be defined in the Turing degrees
with order and relative r.e. relation. A negative result, answering
a question by Miller and Martin, is that there is no quantifierfree
definition for hyperimmunity or array nonrecursiveness in the
language of order and jump. Both results are joint work with Shore.
Speaker: Chris Conidis
Title: Chain Conditions in
Computable Rings, Part II
Abstract: Three years ago in
November 2008 I presented the first part of this talk at this
meeting. In particular, I then set out to examine the reverse
mathematical strength of the statements
1. Every Artinian ring is Noetherian, and
2. Every Artinian ring has finite length (as a module over
itself).
More specifically, I showed that statement 1 is implied by ACA_0 and
implies WKL_0 over RCA_0+I\Sigma_2, while statement 2 is equivalent
to ACA_0 over RCA_0+\BSigma_2. In this talk I will shed
considerably more light on the strength of statement 1, showing that
it is in fact equivalent to WKL_0 over RCA_0+\ISigma_2. The key to
this result lies in a new algebraic approach to proving that the
Jacobson radical of an Artinian ring is nilpotent.
Speaker: Stephen Flood
Title: Reverse mathematics
and a packed Ramsey's theorem.
Abstract: Ramsey's theorem
states that each coloring has an infinite homogeneous set, but these
sets can be arbitrarily spread out. Paul Erdos and Fred Galvin
proved that for each coloring f, there is an infinite set which is
not ``too spread out'' that is not given ``too many'' colors by
f. In this talk, I will give the precise statement of this
packed Ramsey's theorem and discuss my work on its reverse
mathematical strength. In particular, I have shown that this
theorem is equivalent to Ramsey's theorem for each exponentn=\=2,
and that it implies Ramsey's theorem for n=2.
Speaker: Jeff Hirst
Title: Reverse mathematics
and persistent reals
Abstract: The dichotomy
principle asserts that each real number is either less than or equal
to 0 or greater than or equal to 0. The reverse mathematics
subsystem RCA0 can prove dichotomy. On the other hand, given a
sequence of reals, the existence of a set separating them into
disjoint collections of nonpositive and nonnegative reals is
equivalent to the subsystem WKL0 over RCA0. Thus, this sequential
form of dichotomy fails in computable analysis. We will show
how a computable restriction of the sequential form can motivate the
formulation of a constructive restriction of the original
principle. The results in this talk are joint work with
François Dorais and Paul Shafer.
Speaker: Asher Kach
Title: Orders on Computable
TorsionFree Abelian Groups
Abstract: In this talk, we
will discuss the (Turing) degrees of orders on computable
presentations of computable torsionfree abelian groups. After
providing the requisite algebraic background, we will review known
results and discuss new results. In particular, we show the
set of degrees of orders for a fixed computable presentation need
not be upward closed. This new work is joint with Karen Lange
and Reed Solomon.
Previous Seminars:
 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
 Feb 15th 2011. Uri Andrews 
Paola D'Aquino  David Diamondstone  Christopher Porter 
Rebecca Steiner.
 Nov 1st 1011. Mingzhong Cai  Chris Conidis  Stephen Flood 
Jeff Hirst  Asher Kach.
If you haven't
been receiving the announcements, and you would like to be included
in the list, send an email to drh@math.uchicago.edu.