From Abstract to Concrete Gödel's Incompleteness Theorems—Part I

Andrei Popescu and Dmitriy Traytel

16 September 2020

Abstract

We validate an abstract formulation of Gödel's First and Second Incompleteness Theorems from a separate AFP entry by instantiating them to the case of finite sound extensions of the Hereditarily Finite (HF) Set theory, i.e., FOL theories extending the HF Set theory with a finite set of axioms that are sound in the standard model. The concrete results had been previously formalised in an AFP entry by Larry Paulson; our instantiation reuses the infrastructure developed in that entry.
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