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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. |
| 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{http://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. |
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