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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1978, Volume 23, Issue 3, Pages 471–485 (Mi mz8162)

Infinite sums and products of isol integers

V. L. Mikheev

Novosibirsk State University

Abstract: A definition is provided of $k$-fold infinite sums and products of isol integers, and certain properties of such sums and products are proven. The definition is based on the concept of generalized recursive equivalence types, introduced at the beginning of this paper. The validity of the properties, connected with the canonical extensions of functions on isols, is established for arbitrary functions, and not only for general recursive functions, since the generalized recursive equivalence types permit their incorporation without the Nerode metatheorem in the proof of such properties.

Full text: PDF file (1186 kB)

English version:
Mathematical Notes, 1978, 23:3, 255–262

Bibliographic databases:

UDC: 519

Citation: V. L. Mikheev, “Infinite sums and products of isol integers”, Mat. Zametki, 23:3 (1978), 471–485; Math. Notes, 23:3 (1978), 255–262

Citation in format AMSBIB
\Bibitem{Mik78} \by V.~L.~Mikheev \paper Infinite sums and products of isol integers \jour Mat. Zametki \yr 1978 \vol 23 \issue 3 \pages 471--485 \mathnet{http://mi.mathnet.ru/mz8162} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=476464} \zmath{https://zbmath.org/?q=an:0413.03026} \transl \jour Math. Notes \yr 1978 \vol 23 \issue 3 \pages 255--262 \crossref{https://doi.org/10.1007/BF01651442}