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The Godel Incompleteness Theorems (1931) by the Axiom of Choice

EasyChair Preprint 3855

4 pagesDate: July 13, 2020

Abstract

Those incompleteness theorems mean the relation of (Peano) arithmetic and (ZFC) set theory, or philosophically, the relation of arithmetical finiteness and actual infinity. The same is managed in the framework of set theory by the axiom of choice (respectively, by the equivalent well-ordering "theorem'). One may discuss that incompleteness form the viewpoint of set theory by the axiom of choice rather than the usual viewpoint meant in the proof of theorems. The logical corollaries from that "nonstandard" viewpoint the relation of set theory and arithmetic are demonstrated.

Keyphrases: arithmetic, choice, information, set theory, well-ordering

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@booklet{EasyChair:3855,
  author    = {Vasil Penchev},
  title     = {The Godel Incompleteness Theorems (1931) by the Axiom of Choice},
  howpublished = {EasyChair Preprint 3855},
  year      = {EasyChair, 2020}}
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