Local initial segments of the Turing degrees

TL;DR

This paper discusses recent findings on initial segments of the Turing degrees and explores conjectures related to their structure, which have implications for automorphisms of the Turing degrees.

Contribution

It presents recent results on initial segments and proposes conjectures that impact the understanding of automorphisms in the Turing degrees.

Findings

Recent results on initial segments of Turing degrees

Conjectures about initial segments and automorphisms

Implications for the structure of Turing degrees

Abstract

Recent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of non-trivial automorphisms of the Turing degrees are indicated.