Gödel's Theorem is Invalid - Revision history

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	{{Infobox paper		{{Infobox paper
	\| title = ~~G?del~~\'s Theorem is Invalid		\| title = Gödel\'s Theorem is Invalid
	\| url = [https://web.archive.org/web/20250508010737/http://arxiv.org/PS_cache/math/pdf/0510/0510469v1.pdf Link to paper (Internet Archive)]		\| url = [https://web.archive.org/web/20250508010737/http://arxiv.org/PS_cache/math/pdf/0510/0510469v1.pdf Link to paper (Internet Archive)]
	\| author = [[Diego ~~Jos?~~ Arturo Sa]]		\| author = [[Diego José Arturo Sa]]
	\| keywords = [[~~G?del~~]], [[Godel]], [[Goedel]], [[incompleteness]], [[undecidability]], [[theorem]]		\| keywords = [[Gödel]], [[Godel]], [[Goedel]], [[incompleteness]], [[undecidability]], [[theorem]]
	\| published = 2005		\| published = 2005
	\| journal = [[ArXiv]]		\| journal = [[ArXiv]]
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	==Abstract==		==Abstract==

	~~G?del~~'s results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by ~~G?del~~ to prove his undecidability and incompleteness theorems is proved in this paper. This means that those theorems are invalid.		Gödel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Gödel to prove his undecidability and incompleteness theorems is proved in this paper. This means that those theorems are invalid.

	In section 1, a study is carried out on the mathematical induction principle, even though it is not directly relevant to the problem, just to familiarize the reader with the operations that are used later; in section 2 the rule of mathematical induction is introduced, this rule has a metamathematical character; in section 3 the original proof of ~~G?del~~'s undecidability theorem is reproduced, and finally in section 4 the same proof is given, but now with the explicit and formal use of all the axioms; this is needed to be able to use logical resolution. It is shown that the inclusion of the mathematical induction rule causes a contradiction.		In section 1, a study is carried out on the mathematical induction principle, even though it is not directly relevant to the problem, just to familiarize the reader with the operations that are used later; in section 2 the rule of mathematical induction is introduced, this rule has a metamathematical character; in section 3 the original proof of Gödel's undecidability theorem is reproduced, and finally in section 4 the same proof is given, but now with the explicit and formal use of all the axioms; this is needed to be able to use logical resolution. It is shown that the inclusion of the mathematical induction rule causes a contradiction.

	[[Category:Scientific Paper\|g del 's theorem invalid]]		[[Category:Scientific Paper\|g del 's theorem invalid]]

ClaudeBot: ClaudeBot moved page G?del's Theorem is Invalid to Gödel's Theorem is Invalid: Fix mojibake: restore diacritics from explicit per-word resolution

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ClaudeBot moved page G?del's Theorem is Invalid to Gödel's Theorem is Invalid: Fix mojibake: restore diacritics from explicit per-word resolution

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	{{Infobox paper		{{Infobox paper
	\| title = G?del's Theorem is Invalid		\| title = G?del\'s Theorem is Invalid
			\| url = [https://web.archive.org/web/20250508010737/http://arxiv.org/PS_cache/math/pdf/0510/0510469v1.pdf Link to paper (Internet Archive)]
	\| author = [[Diego Jos? Arturo Sa]]		\| author = [[Diego Jos? Arturo Sa]]
	\| keywords = [[G?del]], [[Godel]], [[Goedel]], [[incompleteness]], [[undecidability]], [[theorem]]		\| keywords = [[G?del]], [[Godel]], [[Goedel]], [[incompleteness]], [[undecidability]], [[theorem]]
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	\| num_pages = 20		\| num_pages = 20
	}}		}}

			'''Read the full paper''' [https://web.archive.org/web/20250508010737/http://arxiv.org/PS_cache/math/pdf/0510/0510469v1.pdf here] ''(archived copy — the original link is no longer available)''

	==Abstract==		==Abstract==

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2026-07-20T03:36:25Z

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	{{Infobox paper		{{Infobox paper
	\| title = G?del\'s Theorem is Invalid		\| title = G?del's Theorem is Invalid
	\| author = [[Diego Jos? Arturo Sa]]		\| author = [[Diego Jos? Arturo Sa]]
	\| keywords = [[G?del]], [[Godel]], [[Goedel]], [[incompleteness]], [[undecidability]], [[theorem]]		\| keywords = [[G?del]], [[Godel]], [[Goedel]], [[incompleteness]], [[undecidability]], [[theorem]]

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	In section 1, a study is carried out on the mathematical induction principle, even though it is not directly relevant to the problem, just to familiarize the reader with the operations that are used later; in section 2 the rule of mathematical induction is introduced, this rule has a metamathematical character; in section 3 the original proof of G?del's undecidability theorem is reproduced, and finally in section 4 the same proof is given, but now with the explicit and formal use of all the axioms; this is needed to be able to use logical resolution. It is shown that the inclusion of the mathematical induction rule causes a contradiction.		In section 1, a study is carried out on the mathematical induction principle, even though it is not directly relevant to the problem, just to familiarize the reader with the operations that are used later; in section 2 the rule of mathematical induction is introduced, this rule has a metamathematical character; in section 3 the original proof of G?del's undecidability theorem is reproduced, and finally in section 4 the same proof is given, but now with the explicit and formal use of all the axioms; this is needed to be able to use logical resolution. It is shown that the inclusion of the mathematical induction rule causes a contradiction.

	[[Category:Scientific Paper]]		[[Category:Scientific Paper\|g del 's theorem invalid]]

Maintenance script: Imported from text file

2016-12-30T05:00:17Z

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{{Infobox paper
| title = G?del\'s Theorem is Invalid
| author = [[Diego Jos? Arturo Sa]]
| keywords = [[G?del]], [[Godel]], [[Goedel]], [[incompleteness]], [[undecidability]], [[theorem]]
| published = 2005
| journal = [[ArXiv]]
| num_pages = 20
}}

==Abstract==

G?del's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by G?del to prove his undecidability and incompleteness theorems is proved in this paper. This means that those theorems are invalid.

In section 1, a study is carried out on the mathematical induction principle, even though it is not directly relevant to the problem, just to familiarize the reader with the operations that are used later; in section 2 the rule of mathematical induction is introduced, this rule has a metamathematical character; in section 3 the original proof of G?del's undecidability theorem is reproduced, and finally in section 4 the same proof is given, but now with the explicit and formal use of all the axioms; this is needed to be able to use logical resolution. It is shown that the inclusion of the mathematical induction rule causes a contradiction.

[[Category:Scientific Paper]]