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{http://isa-afp.org/entries/Goedel_HFSet_Semantic.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Goedel_Incompleteness, Incompleteness