Midwest
Computability Seminar
XXV
Part v
The Midwest Computability
Seminar is meeting remotely in the fall of 2020. The recurring Zoom link is:
https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09
Meeting ID: 997 5433 2165
Passcode: midwest
Slides
Panopto
video
YouTube video
This session will be held jointly with the Computability Theory and
Applications Online Seminar.
DATE: Tuesday, October 13th, 2020
TIME: 3:00 - 4:00 PM CDT
SPEAKER: Leszek Kołodziejczyk - University of Warsaw
TITLE: Reverse mathematics of combinatorial principles over
a weak base theory
ABSTRACT: Reverse mathematics studies the strength of axioms
needed to prove various mathematical theorems. Often, the theorems have
the form ∀X ∃Y ψ(X,Y) with
X,Y denoting subsets of ℕ and ψ arithmetical, and
the logical strength required to prove them is closely related to the
difficulty of computing Y given X. In the early decades of
reverse mathematics, most of the theorems studied turned out to be
equivalent, over a relatively weak base theory, to one of just a few
typical axioms, which are themselves linearly ordered in terms of
strength. More recently, however, many statements from combinatorics,
especially Ramsey theory, have been shown to be pairwise inequivalent or
even logically incomparable.
The usual base theory used in reverse mathematics is RCA0,
which
is intended to correspond roughly to the idea of "computable mathematics".
The main two axioms of RCA0 are: comprehension for computable
properties of natural numbers and mathematical induction for c.e.
properties. A weaker theory in which induction for c.e. properties is
replaced by induction for computable properties has also been introduced,
but it has received much less attention. In the reverse mathematics
literature, this weaker theory is known as RCA0*.
In this talk, I will discuss some results concerning the reverse
mathematics
of combinatorial principles over RCA0*. We will
focus mostly
on
Ramsey's theorem and some of its well-known special cases: the
chain-antichain principle CAC, the ascending-descending chain principle
ADS,
and the cohesiveness principle COH.
The results I will talk about are part of a larger project joint with
Marta
Fiori Carones, Katarzyna Kowalik, Tin Lok Wong, and Keita Yokoyama.
Past and Future Sessions
Previous Seminars:
- 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
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.