Lowness for isomorphism, countable ideals, and computable traceability

TL;DR

This paper investigates the structure of degrees low for isomorphism, demonstrating their containment within principal ideals and exploring their independence from computable traceability in hyperimmune-free degrees.

Contribution

It introduces an exact pair construction for countable ideals low for isomorphism and shows their independence from computable traceability in specific degrees.

Findings

Countable ideals low for isomorphism are contained in principal ideals.

Lowness for isomorphism is independent of computable traceability in hyperimmune-free degrees.

An exact pair construction is used to establish ideal containment.

Abstract

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune-free degrees, lowness for isomorphism is entirely independent of computable traceability.