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JOURNALS // Algebra i logika // Archive

Algebra Logika, 2003 Volume 42, Number 1, Pages 3–25 (Mi al14)

This article is cited in 26 papers

Splitting Properties of Total Enumeration Degrees

M. M. Arslanova, I. Sh. Kalimullinb, S. B. Cooperc

a Kazan State University
b N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
c University of Leeds

Abstract: We describe general conditions under which relative splittings and specified diamond embeddings are derivable in the local structure of enumeration degrees (e-degrees). In so doing, we touch upon three basic issues: the possibility for studying properties of Turing degrees via enumeration reducibility; general definability problems and the role of splitting and non-splitting; and (emerging from the techniques developed) the description of new relationships between information content and degree theoretic structure.

Keywords: enumeration degrees, Turing degrees, splitting of degrees.

UDC: 510.5

Received: 30.01.2001


 English version:
Algebra and Logic, 2003, 42:1, 1–13

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