Seminar on Mathematical Logic

Year: 2010

ECTS: 6

Lecturers: Dr. George Barmpalias and Dr. Benedikt Lwe

Meetings: The dates for the meetings for this course will be a proper subset of those mentioned in the schedule. This is because of some conflicts with other courses. These will be: 2Feb, 23Feb, 2Mar, 9Mar, 23Mar, 6Apr, 13 Apr, 20Apr, 27Apr, 4May, 11May, 18May, 25May.

There will be NO meetings on: 9Feb, 16Feb, 16Mar, 30Mar.

Description: The students attending this course will be given a collection of selected results from the areas of Descriptive Set Theory, Algorithmic Randomness and Computability theory. Each student is assigned a topic/result which (s)he is going to master and eventually present it before all students in the class and the two lecturers. Often the preparation and study of a result requires substantial work, especially on covering the background theory on which the result lies upon.

Assesment: Students will be assessed on the basis of their preparation of their presentation and their performance during their talk.

Prerequisites: The project is particularly suitable for those who have some mathematical maturity and can study with some degree of independence. Some interest in definability theory (and in particular Descriptive Set Theory, Algorithmic Randomness and Computability theory) is highly desirable, as well as feeling comfortable with self-study.


Date Topic Speaker
23 Feb 2010 Σ03 and Σ04 determinacy (references 4,7). Martijn Baartse
9 Mar 2010 Cancelled Cancelled
23 Mar 2010 Π11 Uniformization (Kondo) (reference 1) Gabriela Rino
6 Apr 2010 A new proof of Π11 uniformization (Blackwell) (reference 9) Helene Tourigny
13 Apr 2010 First Periodicity Theorem (references 1,8) Zhenhao Li
20 Apr 2010 Second Periodicity Theorem (references 1,8) Purbita Jana
27 Apr 2010 Mauldin's Theorem: the set of nowhere differentiable continuous functions form a Π11-complete set (reference 1). Adam Lesnikowski
4 May 2010 Turing incomparability in Scott sets (reference ). Nicola Di Giorgio
11 May 2010 Extracting information is hard (reference 2) Tom Sterkenburg
18 May 2010 Unprovability of Σ04 determinacy in second order arithmetic (references 5, 10) G. Barmpalias and B. Loewe

Bibliography
Classical Descriptive Set theory
by A. Kechris (Graduate texts in Mathematics)
Extracting information is hard
by J. Miller, to appear in Adv. Math. pdf
Turing incomparability in Scott sets
by A. Kucera and T. Slaman, Proc. Amer. Math. Soc., 135:3723--3731, 2007. Preprint
Proving determinacy
Draft of the unpublished book of D. Martin.
Higher set theory and mathematical practice
by Harvey M. Friedman, Ann. Math. Logic 2 1970/1971 no. 3, 325--357.
Infinite games of perfect information
by Morton Davis, Advances in game theory (1964) 85--101 Princeton Univ. Press, Princeton, N.J.
ZF \vdash Σ04 determinateness
by J. B. Paris, J. Symbolic Logic 37 (1972), 661--667.
ZF \vdash Σ04 determinateness
by J. B. Paris, J. Symbolic Logic 37 (1972), 661--667.
Descriptive set theory
by Y. Moschovakis (Studies in logic and the FOM)
Infinite games and analytic sets
by David Blackwell, Proc. Nat. Acad. Sci. U.S.A. 58 1967 1836--1837
The limits of determinacy in second order arithmetic
by A. Montalban and R. Shore, Preprint

  Last updated: Tuesday, 06 September 2016 Copyright 2016 Barmpalias