Current research on G\"odel's incompleteness theorems

TL;DR

This paper surveys recent research on G"odel's incompleteness theorems, focusing on proof classifications, applicability limits of the theorems, and their implications in mathematical logic.

Contribution

It provides a comprehensive overview of current research directions and limitations related to G"odel's incompleteness theorems.

Findings

Classifications of different proofs of G"odel's theorems

Limits of applicability of the first incompleteness theorem

Limits of applicability of the second incompleteness theorem

Abstract

We give a survey of current research on G\"{o}del's incompleteness theorems from the following three aspects: classifications of different proofs of G\"{o}del's incompleteness theorems, the limit of the applicability of G\"{o}del's first incompleteness theorem, and the limit of the applicability of G\"{o}del's second incompleteness theorem.