Southern Wisconsin Logic Colloquium

Logic Picnic on September 13

Thanks to Turbo Ho, Tamvana Makuluni and Paul Tveite for organizing a wonderful picnic!

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, September 23 4:00 p.m. Turbo Ho, UW Random nilpotent groups (see abstract) cookies/ beverages at 3:30
Tuesday, September 30
(Midwest Computability Seminar,
University of Chicago)
1:00 p.m. Eric Astor, University of Chicago, Illinois TBA depart at 8:30 a.m.
from Van Vleck
loading dock/
lunch at noon in Ryerson/
dinner at 6 TBA
1:35 p.m. Quinn Culver, University of Notre Dame, Indiana TBA
2:30 p.m. Jack Lutz, Iowa State University, Ames TBA
4:10 p.m. Tim McNicholl, Iowa State University, Ames TBA
Sunday, October 5 1:20 p.m. Wim Ruitenburg, Marquette University, Milwaukee, Wisconsin From Boole to Heyting to Visser, and beyond lunch at noon TBA
2:00 p.m. Patricia Blanchette, University of Notre Dame The birth of semantic entailment
3:20 p.m. Jon Fleischmann, University of Wisconsin-Rock County, Janesville U2-sentences and chains of Kripke models (see abstract)
4:20 p.m. Tom Drucker, University of Wisconsin-Whitewater Hijacking Leibniz: What non-standard analysis cannot do
Tuesday, October 14 4:00 p.m. Jim Freitag, University of California-Berkeley TBA cookies/ beverages at 3:30/
dinner at 6 TBA
Tuesday, October 21 4:00 p.m. Howard Becker, UW TBA cookies/ beverages at 3:30
Tuesday, October 28
(Midwest Model Theory Day,
University of Illinois at Chicago)
1:00 p.m. Ward Henson, University of Illinois at Urbana-Champaign TBA depart at 8:30 a.m.
from Van Vleck
loading dock/
lunch at 11:30 at Joy Yee's
(1335 S. Halsted)/
dinner at 5:30 TBA
2:30 p.m. Krzysztof Krupiński, University of Wrocław, Poland TBA
4:00 p.m. Ramin Takloo-Bighash, University of Illinois-Chicago TBA
Tuesday, November 11 4:00 p.m. Reese Johnston, UW TBA (specialty exam) cookies/ beverages at 3:30

Math 873 - Fall 2014 - Recursive Model Theory

Instructor: Uri Andrews

Course Description: This course will serve as a survey of historical and current research in computable model theory. There will be a focus on recursive model theory and the model theory of models of Peano Arithmetic.

Math 975 - Reading Seminar in Logic

Our reading seminar is meeting on Wednesdays at 3:30 in room B231 Van Vleck Hall.

Abstracts of talks

Ho's talk: Random nilpotent groups

We study random nilpotent groups in the well-established style of random groups. Whereas random groups are quotients of the free group by a random set of relators, random nilpotent groups are quotients of a free nilpotent group Np,m by a similarly chosen set of relators.

We establish results about the distribution of rank and step for random nilpotent groups. We compute probabilities for random one-relator quotients of Np,m to be abelian, and we show that for any number of relators, random quotients of N2,m are almost never abelian but not cyclic.

Finally, we describe how to lift results about random nilpotent groups to obtain information about standard random groups. A random nilpotent group is trivial if and only if the corresponding random group is perfect, i.e., is equal to its commutator subgroup. Considering adding relators one by one in a stochastic process, we study the threshold number of relators required. This threshold occurs at |R| = log l, while the expected number of relators required is |R| = log log l. As a corollary, at any positive density, random groups are perfect.

This is joint work with Matt Cordes, Moon Duchin, Yen Duong, and Andrew Sanchez.

Fleischmann's talk: U2-sentences and chains of Kripke models

In the 1950's and 1960's, preservation theorems and model completeness results essentially defined the field of classical model theory. In the 1970's and 1980's, notions of categoricity and stability took over. In the 1990's and 2000's, interest in preservation theorems returned, especially in the context of finite model theory, as this field was recognized as a valuable tool for complexity theory. At the same time, there was also a renewed interest in preservation theorems for non-classical logics, especially those related to theoretical computer science. In 2010, we showed that the classical preservation theorems of Lyndon, Łoś, and Tarski for inverse images of homomorphisms and submodels of classical models can be mirrored in a reasonable way for Kripke models of intuitionistic predicate logic, given reasonable (intuitive) definitions of homomorphism and submodel of Kripke models, which suggested a relativized intuitionistic formula hierarchy Un that is equivalent over the axioms of classical logic to the classical formula hierarchy Π0n. In this talk, we consider the possibility of proving a similar intuitionistic analogue of the classical preservation theorem of Chang, Łoś, and Suszko for unions of chains. Though several reasonable candidates for an intuitionistic formula class U analogous to Π02 exist in the literature, including the class introduced by us in 2010, we show that each of these falls short of the desired unions of chains theorem. This remains an open problem.

This research is joint work with Wim Ruitenburg, Ben Ellison, and Dan McGinn.


Prepared by Steffen Lempp (@math.wisc.edu">lemppmath.wisc.edu)