Locicaly separable algebras in varieties of algebras
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 33-42.

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Let Θ be an arbitrary variety of algebras and H be an algebra in Θ. Along with algebraic geometry in Θ over the distinguished algebra H we consider logical geometry in Θ over H. This insight leads to a system of notions and stimulates a number of new problems. We introduce a notion of logically separable in Θ algebras and consider it in the frames of logically-geometrical relations between different H1 and H2 in Θ. The paper is aimed to give a flavor of a rather new subject in a short and concentrated manner.
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B. Plotkin. Locicaly separable algebras in varieties of algebras. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 33-42. https://geodesic-test.mathdoc.fr/item/BASM_2007_2_a3/

[1] Chang C. C., Keisler H. J., Model Theory, North-Holland Publ. Co., 1973 | MR | Zbl

[2] Grossberg R., “Classification theory for abstract elementary classes”, Logic and Algebra, Contemporary Mathematics, 302, ed. Yi Zhang, AMS, 2002, 165–204 | MR | Zbl

[3] Mac Lane S., Categories for the Working Mathematician, Springer-Verlag, 1971

[4] Myasnikov A., Remeslennikov V., “Algebraic geometry over groups, I”, J. of Algebra, 219:1 (1999), 16–79 | DOI | MR | Zbl

[5] Myasnikov A., Remeslennikov V., “Algebraic geometry over groups. II: Logical foundations”, J. of Algebra, 234:1 (2000), 225–276 | DOI | MR | Zbl

[6] Plotkin B., “Varieties of algebras and algebraic varieties”, Israel Math. Journal, 96:2 (1996), 511–522 | DOI | MR | Zbl

[7] Plotkin B., “Algebras with the same algebraic geometry”, Proceedings of the International Conference on Mathematical Logic, Algebra and Set Theory, dedicated to 100 anniversary of P. S. Novikov, Proceedings of the Steklov Institute of Mathematics, MIAN, 242, 2003, 176–207 ; http://arxiv.org/math.math.GM/0210194 | MR | Zbl

[8] Plotkin B., “Some notions of algebraic geometry in universal algebra”, Algebra and Analysis, 9:4 (1997), 224–248 ; St. Peterburg Math. J., 9:4 (1998), 859–879 | MR | Zbl

[9] Plotkin B., Seven lectures on the universal algebraic geometry, Preprint , 2002, 87 pp. Arxiv: math.GM/0204245 | MR