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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1289–1294
DOI: https://doi.org/10.33048/semi.2019.16.089 (Mi semr1130) 		 
Mathematical logic, algebra and number theory

Generic undecidability of universal theories

A. N. Rybalovab

a Omsk State Technical University, 11, Mira ave., Omsk, 644050, Russia
b Sobolev Institute of Mathematics, 13, Pevtsova str., Omsk, 644043, Russia
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DOI: https://doi.org/10.33048/semi.2019.16.089
Abstract: Generic-case approach to algorithmic problems was suggested by Miasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. In this paper we study generic complexity of undecidable universal theories. We prove that any undecidable universal theory remains generically undecidable (i.e. for almost all inputs).
Keywords: universal theory, generic complexity.
Funding agency Grant number
Russian Science Foundation 19-11-00209
Received January 30, 2019, published September 23, 2019
Bibliographic databases:
Document Type: Article
UDC: 510.652
MSC: 11U99
Language: Russian
Citation: A. N. Rybalov, “Generic undecidability of universal theories”, Sib. Èlektron. Mat. Izv., 16 (2019), 1289–1294
Citation in format AMSBIB
\Bibitem{Ryb19}
\by A.~N.~Rybalov
\paper Generic undecidability of universal theories
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1289--1294
\mathnet{http://mi.mathnet.ru/semr1130}
\crossref{https://doi.org/10.33048/semi.2019.16.089}
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