English

An implication of G\"odel's incompleteness theorem

Logic 2009-05-25 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0904.0342,
  title  = {An implication of G\"odel's incompleteness theorem},
  author = {Hitoshi Kitada},
  journal= {arXiv preprint arXiv:0904.0342},
  year   = {2009}
}

Comments

LaTeX, 50 pages

R2 v1 2026-06-21T12:47:27.308Z