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 Urbana-Champaign 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 13:20-14:10

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 so-called 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:

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 Ra 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 model-theoretic properties (arguably due to Skolem and later rediscovered independently by Weispfenning and Miller), the question of whether the theory of Ra 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 Ra codes many of the Diophantine properties of a. In this talk, I will show that when a is quadratic, the theory of Ra 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 second-order theory of one successor.

Ruitenburg's talk: The coming of the lattares

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 co-author 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)