# An Abstract Formalization of Gödel's Incompleteness Theorems

 Title: An Abstract Formalization of Gödel's Incompleteness Theorems Authors: Andrei Popescu 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. BibTeX: @article{Goedel_Incompleteness-AFP, 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{https://isa-afp.org/entries/Goedel_Incompleteness.html}, 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.