An Abstract Formalization of Gödel's Incompleteness Theorems


Title: An Abstract Formalization of Gödel's Incompleteness Theorems
Authors: Andrei Popescu (a /dot/ popescu /at/ mdx /dot/ ac /dot/ uk) and Dmitriy Traytel
Submission date: 2020-09-16
Abstract: We present an abstract formalization of Gödel's incompleteness theorems. We analyze sufficient conditions for the theorems' applicability to a partially specified logic. Our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser's variation of the first theorem, Jeroslow's variation of the second theorem, and the Swierczkowski–Paulson semantics-based approach. This AFP entry is the main entry point to the results described in our CADE-27 paper A Formally Verified Abstract Account of Gödel's Incompleteness Theorems. As part of our abstract formalization's validation, we instantiate our locales twice in the separate AFP entries Goedel_HFSet_Semantic and Goedel_HFSet_Semanticless.
  author  = {Andrei Popescu and Dmitriy Traytel},
  title   = {An Abstract Formalization of Gödel's Incompleteness Theorems},
  journal = {Archive of Formal Proofs},
  month   = sep,
  year    = 2020,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Syntax_Independent_Logic
Used by: Goedel_HFSet_Semantic, Goedel_HFSet_Semanticless
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.