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Vol 56, No 1 (2017)

Article

Modularity and Distributivity of 3-Generated Lattices with Special Elements Among Generators

Gein A.G., Shushpanov M.P.

Abstract

We consider 3-generated lattices whose generating elements possess properties that are, in a sense, close to modularity or distributivity. Those combinations of these properties are specified that are sufficient for a lattice to be modular, and even distributive.

Algebra and Logic. 2017;56(1):1-12
pages 1-12 views

Algebras of Distributions for Binary Formulas in Countably Categorical Weakly o-Minimal Structures

Emel’yanov D.Y., Kulpeshov B.S., Sudoplatov S.V.

Abstract

Algebras of distributions for binary isolating formulas, generalized commutative monoid. Algebras of distributions for binary isolating formulas over a type for countably categorical weakly o-minimal theories are described, and the generalized commutative property of an algebra of distributions for binary isolating formulas over a pair of types for countably categorical weakly o-minimal theories is characterized in terms of convexity rank.

Algebra and Logic. 2017;56(1):13-36
pages 13-36 views

The Computational Power of Infinite Time Blum–Shub–Smale Machines

Koepke P., Morozov A.S.

Abstract

Functions that are computable on infinite time Blum–Shub–Smale machines (ITBM) are characterized via iterated Turing jumps, and we propose a normal form for these functions. It is also proved that the set of ITBM computable reals coincides with ℝ∩Lωω.

Algebra and Logic. 2017;56(1):37-62
pages 37-62 views

Processes and Structures on Approximation Spaces

Stukachev A.I.

Abstract

We introduce the concept of a computability component on an admissible set and consider minimal and maximal computability components on hereditarily finite superstructures as well as jumps corresponding to these components. It is shown that the field of real numbers Σ-reduces to jumps of the maximal computability component on the least admissible set ℍ????(∅). Thus we obtain a result that, in terms of Σ-reducibility, connects real numbers, conceived of as a structure, with real numbers, conceived of as an approximation space. Also we formulate a series of natural open questions.

Algebra and Logic. 2017;56(1):63-74
pages 63-74 views

Hyperidentities of Quasilinear Clones

Mal’tsev I.A.
Algebra and Logic. 2017;56(1):80-81
pages 80-81 views

Model-Theoretic Aspects of the Theory of Divisible Rigid Soluble Groups

Myasnikov A.G., Romanovskii N.S.
Algebra and Logic. 2017;56(1):82-84
pages 82-84 views

Sessions of the Seminar “Algebra i Logika”

Algebra and Logic. 2017;56(1):85-86
pages 85-86 views

Communications

The Embedding Problem for Computable Projective Planes

Kogabaev N.T.
Algebra and Logic. 2017;56(1):75-79
pages 75-79 views