On effective undecidability and Post's problem

TL;DR

This thesis explores the boundaries of effective undecidability to find new approaches to Post's problem, aiming for more tractable solutions than previous methods by Friedberg and Muchnik.

Contribution

It investigates new notions of effective undecidability to potentially resolve Post's problem more effectively.

Findings

Identifies limitations of current effective undecidability notions

Proposes new approaches to Post's problem

Achieves partial progress towards more tractable solutions

Abstract

In this thesis, we will look at some known and some previously uninvestigated notions of effective undecidability. We try to discover how far we can stretch effective undecidability in the hope to get a more tractable solution to Post's problem, than that of Friedberg and Muchnik.