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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
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
Citation:
A. N. Rybalov, “Generic incompleteness of formal arithmetic”, Sib. Èlektron. Mat. Izv., 12 (2015), 185–189
Linking options:
https://www.mathnet.ru/eng/semr578 https://www.mathnet.ru/eng/semr/v12/p185
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Abstract page: | 271 | Full-text PDF : | 64 | References: | 46 |
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