HIGHER RECURSION THEORY AND SET THEORY

This volume celebrates the research contributions of Professors Theodore A Slaman and W Hugh Woodin, marking their distinguished careers in higher recursion theory and set theory as they approached the milestone of their 65th birthdays in 2019. It originates from the Institute for Mathematical Sciences program, Higher Recursion Theory and Set Theory, held at the National University of Singapore (May 20–June 14, 2019).

The program explored cutting-edge developments in higher recursion theory, set theory, and their intricate interconnections. Topics discussed during the workshop included Martin's conjecture, higher randomness, the HOD conjecture, descriptive inner model theory, and the Ultimate-L program.

This volume presents 15 peer-reviewed contributions by leading experts in the field, offering a comprehensive overview of recent advances in higher recursion theory and set theory, with a focus on their dynamic interactions.

Contents:
Elementary Theories of Rogers Semilattices in the Analytical Hierarchy (Nikolay Bazhenov and Manat Mustafa)Realizing Computably Enumerable Degrees in Separating Classes (Peter Cholak, Rod Downey, Noam Greenberg and Daniel Turetsky)On σ-complete Uniform Ultrafilters (Moti Gitik)More on Bases of Uncountable Free Abelian Groups (Noam Greenberg, Linus Richter, Saharon Shelah and Dan Turetsky)Turing Degrees of Hyperjumps (Hayden R Jananthan and Stephen G Simpson)Pseudojump Inversion in Special II01 Classes of Sets (Hayden R Jananthan and Stephen G Simpson)A Tractable Case of the Turing Automorphism Problem: Bi-uniformly E0-invariant Cantor Homeomorphisms (Bjørn Kjos-Hanssen)An Introduction to AD+ (Paul B Larson)On the Borelness of Upper Cones of Hyperdegrees (Benoit Monin and Liang Yu)A New Game Metatheorem for Ash–Knight Style Priority Constructions (Antonio Montalbán)An I0 Analogue of an AD Theorem (Xianghui Shi)Type Omitting Theorems for Fragments of Second Order Logics: Classical and Modal (Richard A Shore)Mouse Pairs and Suslin Cardinals (John R Steel)A Worked Example of the Functional Interpretation (Henry Towsner)Complete Determined Borel Sets and Measurability (Linda Westrick)
Readership: Researchers, graduate and undergraduate students in the areas of mathematical logic and foundation of mathematics, especially in set theory and recursion theory.