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Algebra Logika, 2017, Volume 56, Number 3, Pages 348–353 (Mi al795)  

Generic Gödel's incompleteness theorem

A. N. Rybalovab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia
b Omsk State Technical University, pr. Mira 11, Omsk, 644050 Russia

Abstract: Gödels incompleteness theorem asserts that if formal arithmetic is consistent then there exists an arithmetic statement such that neither the statement nor its negation can be derived from the axioms of formal arithmetic. Previously [Sib. El. Mat. Izv., 12 (2015), 185–189], it was proved that formal arithmetic remains incomplete if, instead of the set of all arithmetic statements, we consider any set of some class of “almost all” statements (a class of socalled strongly generic subsets). This result is strengthened as follows: formal arithmetic is incomplete for any generic subset of arithmetic statements (i.e., a subset of asymptotic density 1).

Keywords: Gödels theorem, formal arithmetic, generic subsets of arithmetic statements.

Funding Agency Grant Number
Russian Science Foundation 14-11-00085
Supported by Russian Science Foundation, project No. 14-11-00085.


DOI: https://doi.org/10.17377/alglog.2017.56.304

Full text: PDF file (117 kB)
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English version:
Algebra and Logic, 2017, 56:3, 232–235

Bibliographic databases:

UDC: 510.5
Received: 13.04.2016
Revised: 16.06.2016

Citation: A. N. Rybalov, “Generic Gödel's incompleteness theorem”, Algebra Logika, 56:3 (2017), 348–353; Algebra and Logic, 56:3 (2017), 232–235

Citation in format AMSBIB
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