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For a wide category K, we introduce the notions of a K-precomplete map and of a K-subspace. Based on these, we create a uniform method for constructing K-completions of T0-spaces.
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...
Let G be a countable saturated model of the theory 𝔗m of divisible m-rigid groups. Fix the splitting G1G2 . . .Gm of a group G into a semidirect product of Abelian groups. With each tuple (n1, . . . , nm) of nonnegative integers we associate an ordinal α = ωm−1nm+ . . . + ωn2 + n1 and denote by...
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