GODEL'S INCOMPLETENESS THEOREM AND COMPLETENESS AXIOM
Alexandr Vladimirovich Bessonov
Institute of Philosophy and Law, Siberian Branch of the Russian Akademy of Sciences, Novosibirsk, 630090, Russia
Keywords: Godel's incompleteness theorem, formalization of (non)provability, provability predicate, falsifiability predicate, solvability predicate, unsolvability, completeness axiom
Abstract
The article considers K. Godel's incompleteness theorem of formal Dedekind-Peano arithmetic in respect to various non-Godel means of formalizing (non)provability. A solvability predicate is introduced, using which we can frame up a formula that formally expresses the completeness of arithmetic and prove its insolvability. It followed that the addition of the axiom of completeness to formal arithmetic results in a consistent system which contradicts, in a sense, Godel’s first incompleteness theorem.
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