Southern Wisconsin Logic Colloquium

Logic Picnic

Thanks to Dan Rosendorf for organizing a great picnic, and to Kostas Beros and Manli Miller for grilling!

SWLC Schedule

Refreshments will be served in the 9th floor lounge a half hour before talks, or immediately following the 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, May 13
(tentative date) 		2:30 p.m. Dilip Raghavan MADness in Set Theory (thesis defense, see abstract) wine/cheese etc. at 3:30 p.m. and 5 p.m.
4:00 p.m. James Hunter Higher-order reverse topology (thesis defense, see abstract)

Math 873 in fall 2008

Title:Advanced Topics in Foundations: Effective Randomness

Instructor: Joe Miller

Prereq: Math 773

Description: Martin-Löf defined the random binary sequences as those which pass certain effectively presented statistical tests. Levin and Chaitin both used a form of Kolmogorov complexity to characterize Martin-Löf randomness in terms of incompressibility, while Schnorr gave a characterization in terms of betting games. Thus we have three equivalent formulations of effective randomness which can be seen as formalizing three different fundamental intuitions: random sequences are "unremarkable", "incompressible" and "unpredictable". This course will introduce Kolmogorov complexity, effective randomness, effective Hausdorff dimension, triviality and lowness. We will go from the basic definitions to recent results and open questions of current interest. Students should have had an introductory course in computability theory.

Abstracts of talks

Raghavan's talk: MADness in set theory

I plan to summarize the contents of my three papers "There is a Van Douwen MAD family", "Strongly and Very MAD families of Functions" and "Consistency of no Gregory Trees with large Continuum". These are all available on my website. They also constitute my thesis. As time permits, I will outline the ideas in the proof of the result in the third paper. That paper is joint work with Kunen.

Hunter's talk: Higher-order reverse topology

Traditional reverse-mathematics limits itself to examining second-order sentences - statements involving only natural numbers and sets of natural numbers. For reverse topology, this limitation effectively limits the scope of discourse to countably-based topologies on spaces of size continuum - where the relation determining whether a point is in some open set is given by some fixed second-order formula. By instead starting with a base theory in all finite types, we are able to analyze the strength of certain third-order topological statements that cannot be expressed in a second-order language.

Prepared by Steffen Lempp (lempp@math.wisc.edu)