An implication of Gödel's incompleteness theorem

Details An implication of Gödel's incompleteness theorem An implication of Gödel's incompleteness theorem

2009-04-02

arxiv.org/abs/0904.0342v1

International Journal of Pure and Applied Mathematics, 52, No. 4 (2009), 511-567.

Mathematics

Logic

LaTeX, 50 pages

Scientific paper

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.

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