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.
DATE: Tuesday, October 24, 2017.
PLACE: Ryerson Hall 352 (the
Barn), The University of
1100 East 58th Street, Chicago, IL 60637.
- Noah Schweber - University of Wisconsin
- Don Stull - Iowa State University
- Dan Turetsky - University of Notre Dame
- Rose Weisshaar - University of Notre Dame
- 12:00 - 1:00: Lunch
- 1:00 - 1:50: Noah Schweber
- 2:00 - 2:50: Don Stull
- 3:30 - 4:00: Rose Weisshaar
- 4:10 - 5:00: Dan Turestky
- 5:30 Dinner at Nella,
1125 E. 55th St.
Title: Computability and Banach-Mazur games
Abstract: We'll look at some questions around Banach-Mazur games. On the
pure computability-theoretic side, after establishing the effectiveness of
some basic facts about Banach-Mazur games we classify the functions
computable from all winning strategies for some Banach-Mazur game as
the hyperarithmetic sets, using an analogue of Hechler forcing for
strategies. On the reverse mathematical side, we parallel this by showing
that Borel Banach-Mazur determinacy is equivalent to ATR0, and
equivalence goes "level-by-level;" by contrast, we also show that there is
Turing ideal satisfying lightface
Σ11-Banach-Mazur determinacy but
not containing 0(ω), this time using an analogue of
forcing for building strategies.
Title: Effective dimension of points on lines
Abstract: This talk will cover recent work using Kolmogorov complexity to
study the dimension of points on lines in the Euclidean plane and its
application to important questions in fractal geometry. In particular, we
will show that this work strengthens the lower bounds of the dimension of
Furstenberg sets. We will also discuss future research and open problems in
this area. This talk is based on joint work with Neil Lutz.
Title: C.e. equivalence relations and the linear orders they
Abstract: Quotient structures are well studied. In the case of linear
orders, it is known that the order-types realized by c.e. quotient
structures are precisely those realized by Δ02
linear orders. We
come at this from a different perspective, by considering, for each c.e.
equivalence relation, which order-types can be realized as a quotient by
that equivalence relation. We study the relationship between
computability-theoretic properties of the equivalence relation and the
algebraic properties of the order-types it can realize. We also define a
pre-order on equivalence relations by comparing the collection of
order-types realized in each.
Title: Countable ω-models of KP and paths through computable
Abstract: It is well known that the Π01 class CPA
⊆ 2ω of completions of Peano arithmetic is universal among
nonempty Π01 subsets of Cantor space. When we consider Π01
subsets of Baire space, however, there is no such universal example. In this
talk, we consider a Π01 class CKP ⊆
ωω whose paths compute the complete diagrams of countable
ω-models of Kripke-Platek set theory (KP). We develop an analogy
between how elements of CPA and CKP try to
compute members of nonempty Π01 subsets of Cantor space and Baire
space, respectively, and we examine how this analogy breaks down. This is
joint work with Julia Knight and Dan Turetsky.
If you haven't
been receiving the announcements and would like to be included
in the list, send an email to email@example.com.