Capita Selecta: Axiomatic Set Theory, Model Theory

Year: 2009-2010

Selected topic: Descriptive Set theory

Lecturer: George Barmpalias

Lectures: Mondays 13:00

Assesment: 80% Homework + 20% exam

Description: It is well known that when one studies arbitrary subsets of the real numbers one runs into many pathologies (non-measurable sets) and independent problems (the Continuum Hypothesis). In Descriptive Set Theory we try to avoid these pathologies by concentrating on natural classes of well-behaved sets of reals, like Borel sets or projective sets (the smallest class of sets containing Borel sets and closed under projections from higher dimensional spaces). While this is a restricted class of sets it includes most of the sets that arise naturally in mathematical practice.

Bibliography: Recursive aspects of descriptive set theory, by R. Mansfield and G. Weitkamp (Oxford logic guides) Descriptive set theory, by Y. Moschovakis (Studies in logic and the FOM) Classical descriptive set theory, by A. Kechris (Graduate texts in Mathematics) Descriptive set theory notes, by David Marker

Slides: Lectures 1-8                Lectures 9-15

Assignments: Assignment 1 (due 12th Oct) Assignment 2 (due 20th Oct) Assignment 3 (due 2nd Nov) Assignment 4 (due 9th Nov) Assignment 5 (due 23th Nov) Assignment 6 (due 7th Dec) Assignment 7 (due 14th Dec)