Winter 2011

This term we are holding two seminar series. On Tuesday we will have an introductory-level seminar teaching model and recursion/computability theory. On Thursday we will have the research-level seminar. Each is held 11:00-12:00 in Moore 202, and all are welcome.

Introductory Logic Seminar

Tuesdays at 11:00 am in Moore 202.

Date	Speaker	Title
Jan 18		Organizational Meeting
Jan 25	Rebecca Weber	Introduction to Model Theory What is a model? Examples and properties. No logic prerequisites. Handout (amended from copy distributed in seminar).
Feb 1	Nathan McNew	Introduction to Model Theory 2: Definability Handout
Feb 8	Rebecca Weber	Introduction to Model Theory 3: Elimination of quantifiers, Skolemization, and properties of models Handout
Feb 15	Seth Harris	Introduction to Relative Computability: Oracle computation, Turing degrees, and a proof of the existence of two incomparable degrees.
Feb 22	Seth Harris	Introduction to the Arithmetic Hierarchy: definitions and relationship to Turing degrees.
Mar 1	Seth Harris	Index Sets: definitions, Rice's Theorem, connections to the arithmetic hierarchy.

Logic Seminar

Thursdays at 11:00 am in Moore 202.

Date	Speaker	Title
Jan 27	Rebecca Weber Dartmouth College	Automorphisms, invariance, and lowness Jump classes (high_n and low_n) are collections of computably enumerable sets defined in terms of their power as oracles. Once we have those we can look at how they behave within the algebraic structure of c.e. sets ordered by inclusion, and in particular what happens to them when automorphisms are applied. The low (or low_1) sets are different from the rest of the lot and I have ongoing work with Peter Cholak investigating them. This series of talks will introduce the field and discuss the status quo.
Feb 3	Rebecca Weber Dartmouth College	Automorphisms, invariance, and lowness 2
Feb 10	Rebecca Weber Dartmouth College	Automorphisms, invariance, and lowness 3
Feb 17	Johanna Franklin Dartmouth College	Randomness and ergodic theory, part 1 I'll explain the fundamentals of ergodic theory and introduce randomness from this perspective. To do so, I'll describe what it means for a metric space to be computable and how we can talk about randomness in a general computable probability space. Towards the end, I'll present one of the earliest results in the area, proven by Kucera.
Feb 24	Johanna Franklin Dartmouth College	Randomness and ergodic theory, part 2 This week, I'll present more recent work on the relationships of ergodic theorems to randomness notions, including some of my own work (joint with Noam Greenberg, Joseph Miller, and Keng Meng Ng).
Mar 3	Johanna Franklin Dartmouth College	Randomness and ergodic theory, part 3 A proof of the theorem from the end of the previous talk, characterizing randomness in terms of Birkhoff points (via Poincare points).