Relative to any non-hyperarithmetic set

TL;DR

This paper constructs a linear ordering whose degree spectrum includes exactly all non-hyperarithmetic degrees and demonstrates that degree spectra can differentiate between measure and category.

Contribution

It introduces a linear ordering with a degree spectrum precisely matching all non-hyperarithmetic degrees and shows spectra can distinguish measure from category.

Findings

Degree spectrum of a linear ordering equals all non-hyperarithmetic degrees.

Degree spectra can differentiate measure from category.

Established a new connection between degree spectra and descriptive set theory.

Abstract

We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.