A Reunion of Godel, Tarski, Carnap, and Rosser

TL;DR

This paper unifies several foundational theorems in logic—Godel's Incompleteness, Tarski's Undefinability, Carnap's Diagonal Lemma, and Rosser's Incompleteness—highlighting their common techniques and relationships.

Contribution

It provides a unified framework connecting key logical theorems, demonstrating their shared proof techniques and conceptual links.

Findings

Identifies common proof techniques among the theorems

Shows how these theorems are interconnected

Provides a unified perspective on foundational logic results

Abstract

We unify Godel's First Incompleteness Theorem (1931), Tarski's Undefinability Theorem (1933), Godel-Carnap's Diagonal Lemma (1934), and Rosser's (strengthening of Godel's first) Incompleteness Theorem (1936), whose proofs resemble much and use almost the same technique.