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A Mechanised Proof of G\"odel's Incompleteness Theorems using Nominal Isabelle
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An Isabelle/HOL formalisation of G\"odel's two incompleteness theorems is presented. The work follows \'Swierczkowski's detailed proof of the theorems using hereditarily finite (HF) set theory. Avoiding the usual arithmetical encodings of syntax eliminates the necessity to formalise elementary number theory within an embedded logical calculus. The Isabelle formalisation uses two separate treatments of variable binding: the nominal package is shown to scale to a development of this complexity, while de Bruijn indices turn out to be ideal for coding syntax. Critical details of the Isabelle proof are described, in particular gaps and errors found in the literature.
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Cited by 1 Pith paper
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HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement
A dual-model framework that extracts proof sketches from whole-proof candidates and refines them with a tactic model and Sledgehammer, reaching 59.4 percent on miniF2F in Isabelle.
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