Enumeration Order Reducibility

TL;DR

This paper introduces a new reducibility concept based on the enumeration orders of recursively enumerable sets, aiming to deepen understanding of their structural relationships.

Contribution

It defines a novel reducibility notion rooted in enumeration orderings, expanding the theoretical framework of computability and set reducibility.

Findings

Defines enumeration order reducibility for r.e. sets

Establishes properties and implications of the new reducibility

Provides theoretical insights into the structure of r.e. sets

Abstract

In this article we define a new reducibility based on the enumeration orders of r.e. sets.