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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2023 Number 5, Pages 96–100 (Mi ivm9883)

This article is cited in 1 paper

Brief communications

Effectively infinite classes of numberings of computable families of reals

M. Kh. Faizrahmanov

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: Results on the effective infinity of classes of all (single-valued) numberings of families of all left-c.e. and all Martin-Löf random left-c.e. reals are presented, as well as sufficient conditions for the effective infinity of classes of numberings of families of computably enumerable sets aimed at obtaining them.

Keywords: computable numbering, single-valued numbering, positive numbering, effective infinity, left-c.e. real.

UDC: 510.5

Received: 09.03.2023
Revised: 09.03.2023
Accepted: 29.03.2023

DOI: 10.26907/0021-3446-2023-5-96-100



© Steklov Math. Inst. of RAS, 2024