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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 732–736
DOI: https://doi.org/10.17377/semi.2017.14.062
(Mi semr819)
 

Mathematical logic, algebra and number theory

Generic Kleene fixed point theorem

A. N. Rybalovab

a Omsk State University, prospekt Mira 55A, Omsk 644077, Russia
b Sobolev Institute of Mathematics, Pevtsova str. 13, Omsk 644043, Russia
References:
Abstract: Kleene's fixed point theorem states that any algorithmic mapping $\mathcal{A}$ of the set of Turing machines to the set of Turing machines has a fixed point: there is a Turing machine $M$ such that machine $\mathcal{A}(M)$ computes the same function as $M$. In this paper we prove a generic analog of this theorem: any algorithmic mapping $\mathcal{A}$ of a set of “almost all” Turing machines to the set of Turing machines has a fixed point.
Keywords: Kleene fixed point theorem, generic computability.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00577
Received April 26, 2017, published August 1, 2017
Bibliographic databases:
Document Type: Article
UDC: 510.57
MSC: 11U99
Language: Russian
Citation: A. N. Rybalov, “Generic Kleene fixed point theorem”, Sib. Èlektron. Mat. Izv., 14 (2017), 732–736
Citation in format AMSBIB
\Bibitem{Ryb17}
\by A.~N.~Rybalov
\paper Generic Kleene fixed point theorem
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 732--736
\mathnet{http://mi.mathnet.ru/semr819}
\crossref{https://doi.org/10.17377/semi.2017.14.062}
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