This article is cited in 7 papers

Brief communications

A note on $\Delta_2^0$-spectra of linear orderings and degree spectra of the successor relation

A. N. Frolov

Chair of Higher Mathematics and Mathematical Modeling, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: In this paper we construct linear orderings whose $\Delta_2^0$-spectra coincide with classes of all high$_0$ and high$_1$ degrees, respectively. We also prove that there exists a computable linear ordering such that its degree spectrum of the successor relation coincides with a fixed nonempty class of degrees which represents a $\Sigma_1^0$-spectrum of some $\emptyset'$-computable linear ordering.

Keywords: linear orderings, spectra, degree spectra of the successor relation.

UDC: 510.53+512.562

Presented by the member of Editorial Board: M. M. Arslanov
Received: 17.05.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:11, 65–68

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