Enayat Theories

TL;DR

This paper investigates whether a finitely axiomatized consistent sequential theory can interpret itself along with Tarski biconditionals, providing a framework and discussing related conjectures.

Contribution

It introduces a foundational framework for analyzing Enayat's problem and explores the implications of including Tarski biconditionals in such theories.

Findings

Connected the problem to relevant conjectures

Outlined solution attempts and their limitations

Discussed implications of uniform biconditionals

Abstract

In this paper we study solution attempts for a problem posed by Ali Enayat: can there be a finitely axiomatized consistent sequential theory that interprets itself plus the (sentential or non-uniform) Tarski biconditionals? We provide a basic framework for the study of this question and discuss some solution attempts. We connect the question with some interesting conjectures. We briefly touch upon what happens if we consider uniform biconditionals.