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Restrictions on the degree spectra of algebraic structures

โœ Scribed by I. Sh. Kalimullin


Publisher
SP MAIK Nauka/Interperiodica
Year
2008
Tongue
English
Weight
209 KB
Volume
49
Category
Article
ISSN
0037-4466

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Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this questi

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We show that for every computably enumerable (c.e.) degree aยฟ0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is {0; a}, thus answering a question of Goncharov and Khoussainov (Dokl. Math. 55 (1997) 55-57). We also show