F. Rakymzhankyzy, N. A. Bazhenov, A. A. Issakhov, B. S. Kalmurzayev
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Minimal Generalized Computable Numberings and Families of Positive Preorders
We study A-computable numberings for various natural classes of sets. For an arbitrary oracle A≥T0′, an example of an A-computable family S is constructed in which each A-computable numbering of S has a minimal cover, and at the same time, S does not satisfy the sufficient conditions for the existence of minimal covers specified in [Sib. Math. J., 43, No. 4, 616-622 (2002)]. It is proved that the family of all positive linear preorders has an A-computable numbering iff A′≥T0". We obtain a series of results on minimal A-computable numberings, in particular, Friedberg numberings and positive undecidable numberings.
期刊介绍：
This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions.
Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences.
All articles are peer-reviewed.
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