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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2015, Volume 12, Pages 185–189
DOI: https://doi.org/10.17377/semi.2015.12.015
(Mi semr578)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical logic, algebra and number theory

Generic incompleteness of formal arithmetic

A. N. Rybalov

Omsk State Technical University, prospekt Mira 11, Omsk 644050, Russia
Full-text PDF (453 kB) Citations (2)
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Abstract: Famous Gödel's incompleteness theorem states that formal arithmetic (if it is consistent) has a statement that is unprovable and incontrovertible by any recursive systems of axioms. In this paper we prove that Gödel's theorem remains true if we restrict the set of all arithmetic statements by some natural subsets of “almost all” statements (so called strongly generic sets).
Keywords: formal arithmetic, generic complexity.
Received July 10, 2014, published March 14, 2015
Document Type: Article
UDC: 510.652
MSC: 11U99
Language: Russian
Citation: A. N. Rybalov, “Generic incompleteness of formal arithmetic”, Sib. Èlektron. Mat. Izv., 12 (2015), 185–189
Citation in format AMSBIB
\Bibitem{Ryb15}
\by A.~N.~Rybalov
\paper Generic incompleteness of formal arithmetic
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 185--189
\mathnet{http://mi.mathnet.ru/semr578}
\crossref{https://doi.org/10.17377/semi.2015.12.015}
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  • https://www.mathnet.ru/eng/semr/v12/p185
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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