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

 Title: From Abstract to Concrete Gödel's Incompleteness Theorems—Part I Authors: Andrei Popescu and Dmitriy Traytel Submission date: 2020-09-16 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. BibTeX: @article{Goedel_HFSet_Semantic-AFP, author = {Andrei Popescu and Dmitriy Traytel}, title = {From Abstract to Concrete Gödel's Incompleteness Theorems—Part I}, journal = {Archive of Formal Proofs}, month = sep, year = 2020, note = {\url{https://isa-afp.org/entries/Goedel_HFSet_Semantic.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Goedel_Incompleteness, Incompleteness Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.