Southern Wisconsin Logic Colloquium
SWLC Schedule
Refreshments will be served in the 9th floor lounge a half hour before
talks. Please check the schedule below. All talks will be in 901 Van Vleck
Hall unless stated otherwise.
Date
 Time
 Speaker
 Title
 Cookies,
dinner, etc.

Tuesday, April 7
 4:00 p.m.
 Philipp
Hieronymi, University of Illinois at UrbanaChampaign
 Expansions of the ordered additive group of real numbers by two
discrete subgroups (see abstract)
 cookies/juice at 3:30/ dinner at 6
at Great
Dane Pub (123 E. Doty St.)

Tuesday, April 14 (tentative)
 4:00 p.m.
 Wim Ruitenburg,
Marquette University, Milwaukee, Wisconsin
 The coming of the lattares (see abstract)
 cookies/juice at 3:30

Tuesday, April 21
 4:00 p.m.
 TBA
 TBA
 cookies/juice at 3:30

Tuesday, April 28
 4:00 p.m.
 Iván Ongay
Valverde, UW
 TBA (specialty exam)
 cookies/juice at 3:30

Tuesday, May 5
 4:00 p.m.
 Ethan
McCarthy, UW
 TBA (specialty exam)
 cookies/juice at 3:30

Tuesday, September 8
 4:00 p.m.
 TBA
 TBA
 cookies/juice at 3:30

Tuesday, September 15
 4:00 p.m.
 TBA
 TBA
 cookies/juice at 3:30

Tuesday, September 22
 4:00 p.m.
 TBA
 TBA
 cookies/juice at 3:30

Tuesday, September 29
 4:00 p.m.
 TBA
 TBA
 cookies/juice at 3:30/ dinner at 6 TBA

Tuesday, October 6
 4:00 p.m.
 Henry Townser,
University of Pennsylvania, Philadelphia
 TBA
 cookies/juice at 3:30/ dinner at 6 TBA

Math 873  Fall 2015  Topics in Logic  Medvedev and Muchnik Degrees
Instructor: Rutger Kuyper
Prerequisites: Math 770, and Math 773 or concurrent registration
in Math 773
Time and Place: MWF 13:2014:10
Textbook: none
Course Description:
The Medvedev and Muchnik degrees are extensions of the Turing degrees studied
in computability theory. Both of these structures also have nice substructures,
namely, the degrees of the socalled effectively closed sets, which form an
analogue to the computably enumerable degrees studied in the Turing degrees.
We will discuss various aspects of these structures. In particular, we will
cover the following topics, including their necessary prerequisites:
 Definability of substructures
 Automorphisms
 Embeddability
 Filters and ideals
 Density
 Connections to intuitionistic logic
 Complexity
Math 975  Reading Seminar in Logic
Our reading seminar is meeting on Thursdays at 3:30 in B325 (spring) and
B119 (fall) Van Vleck Hall.
Abstracts of talks
Hieronymi's talk:
Expansions of the ordered additive group of real numbers by two
discrete subgroups
Let a be real number. Denote by R_{a} the expansion of the ordered
additive group of real numbers by a predicate for Z and aZ, where Z is the
set of integers. Although it is well known that the expansion of the ordered
additive group of real numbers by just a predicate for Z has a decidable
theory and other desirable modeltheoretic properties (arguably due to
Skolem and later rediscovered independently by Weispfenning and Miller), the
question of whether the theory of R_{a} is decidable even for some
irrational number a has been open for a long time. The interest in these
structures arises among other things from the observation that the structure
R_{a} codes many of the Diophantine properties of a. In this talk,
I will show that when a is quadratic, the theory of R_{a} is decidable.
The proof of this statement
depends crucially on the periodicity of the continued fraction expansion of
a and combines classical tools from the theory of Diophantine approximations
(in particular, Ostrowski representations) with Büchi's celebrated theorem
about the decidability of the monadic secondorder theory of one successor.
There is a universal class of structures that are lattices with top and a
special arrow, and which generalizes the notion of Heyting algebra `without'
bottom element. With coauthor Mohammad Ardeshir, we name these structures
lattares (stress on ta). We give some examples of lattares,
and show that they have a nontrivial theory.
Prepared by
Steffen Lempp
(@math.wisc.edu">lemppmath.wisc.edu)