Low, Superlow, and Superduperlow Sets: An Exposition of a Known But Not Well-Known Result

TL;DR

This paper clarifies and presents proofs for the known but not widely recognized result that superduperlow sets are decidable, by providing two unpublished proofs from notable researchers.

Contribution

It offers two unpublished proofs demonstrating that superduperlow sets are decidable, enhancing understanding of the hierarchy of low sets.

Findings

Superduperlow sets are decidable.

Provides two unpublished proofs of the main result.

Abstract

A set is low if A' \le_T HALT. A set is superlow if A' \le_tt HALT. A set is superduperlow if A' \le_btt HALT. While it was known that any superduperlow is decidable it does not seem to be well known. We include two unpublished proofs of this result: One from Carl Jockush and one from Frank Stephan.