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arXiv:0904.0342 [math.LO]AbstractReferencesReviewsResources

An implication of Gödel's incompleteness theorem

Hitoshi Kitada

Published 2009-04-02Version 1

A proof of G\"odel's incompleteness theorem is given. With this new proof a transfinite extension of G\"odel's theorem is considered. It is shown that if one assumes the set theory ZFC on the meta level as well as on the object level, a contradiction arises. The cause is shown to be the implicit identification of the meta level and the object level hidden behind the G\"odel numbering. An implication of these considerations is stated.

Comments: LaTeX, 50 pages
Journal: International Journal of Pure and Applied Mathematics, 52, No. 4 (2009), 511-567.
Categories: math.LO
Subjects: 03F40, 03F15, 03B25, 03E99
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