Priority arguments via true strages

TL;DR

This paper introduces a variation of Ash's η-system, providing a new proof of Ash's metatheorem and extending results on pairs of structures in computability theory.

Contribution

It presents a novel variation of Ash's η-system, offers a new proof of Ash's metatheorem, and generalizes existing theorems on pairs of structures.

Findings

New variation of Ash's η-system

Alternative proof of Ash's metatheorem

Generalization of theorems on pairs of structures

Abstract

We describe a variation of Ash's $\eta$-system, and give a new proof of Ash's metatheorem. As an application, we prove a generalization of Ash and Knight's theorem on pairs of structures.