From omega to Omega

Overview

Computability theory and set theory are two branches of mathematical logic. Both originated from questions about the consistency and decidability of mathematics: modern set theory and logic are based on a response to the foundational paradoxes of Russell and Frege; the formalization of computability was used by Gödel in his negative result regarding Hilbert’s programme, namely his incompleteness theorem. There are strong ties between the two subjects, via the study of definability. This has led leading researchers such as Theodore Slaman to view both fields as lying at two ends of a continuum. Recent results have revealed new and exciting connections between computability theory and set theory.

This workshop will bring both computability theorists and set theorists together and develop further connections between the two fields.

The program will focus on, but not limited to, the following topics:

1. Algorithmic randomness and analysis
2. Reverse mathematics and effective content of combinatorial principles
3. Forcing axioms and the axiom star (*)
4. New methods in forcing
5. Descriptive inner model theory, the core model induction and the mouse set conjecture