Martin's conjecture for regressive functions on the hyperarithmetic degrees

2023/06/09 by Lutz, Patrick
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2306.05746

Abstract

We answer a question of Slaman and Steel by showing that a version of Martin's conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin's conjecture, consists of showing that we can always reduce to the case of a continuous function.

Related

• Part 1 of Martin's Conjecture for order-preserving and measure-preserving functions
• Martin's Conjecture in the Enumeration Degrees
• The uniform Martin's conjecture for many-one degrees
• Uniform Martin's conjecture, locally
• Turing Degrees of Hyperjumps