Mechanizing Gödel's incompleteness Theorems and Provability Logic

2026-09-12

AI Summary

该研究使用Lean 4定理证明器机械化证明了哥德尔的不完备性定理、Solovay关于GL系统的算术完备性定理及相关结果。

Abstract

We mechanized proof of Gödel's first and second incompleteness theorems, Solovay's arithmetical completeness theorem of \mathbf{GL}, and related results in the Lean 4 theorem prover.

Problem

• Gödel's incompleteness theorems
• Solovay's arithmetical completeness
• GL

Innovation

• Gödel's incompleteness Theorems
• Solovay's arithmetical completeness
• Lean 4 theorem prover