Higher Recursion Theory and Set Theory

Overview

By “higher recursion theory”, we mean the part of recursion theory that either focuses on subsets of the natural numbers beyond arithmetical sets or studies the theory of computability or definability on domains beyond the set of natural numbers. For example, the former includes the study of hyperarithmetic sets and descriptive set theory, while the latter includes alpha-recursion theory and e-recursion theory which study computability theory on ordinals and aspects of the fine structure theory of the constructible universe L and Q theory. Although we did not mention specific areas of “set theory” in the title, we intend to focus on topics in set theory that have close connections with definability, for example Woodin’s program on ultimate L, the HOD conjecture, and descriptive inner model theory.

Higher recursion theory and the parts of set theory mentioned above have a long history of interaction. The interaction continues until now. This workshop would provide a valuable chance for these communities to interact and work on shared concerns in these areas.

The program will focus on the following topics:

• Martin’s Conjecture;
• higher randomness;
• the HOD conjecture;
• descriptive inner model theory (DIMT), the core model induction and the mouse set conjecture; and
• suitable extender sequences and Ultimate L.