Download PDFOpen PDF in browserThe Godel Incompleteness Theorems (1931) by the Axiom of ChoiceEasyChair Preprint 38554 pages•Date: July 13, 2020AbstractThose 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 wellordering "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, wellordering
