Geodesic
Some logical invariants of algebras and logical relations between algebras
Algebra i analiz, Tome 19 (2007) no. 5, pp. 214-245.

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Let $\Theta$ be an arbitrary variety of algebras and $H$ an algebra in $\Theta$. Along with algebraic geometry in $\Theta$ over the distinguished algebra $H$, a logical geometry in $\Theta$ over $H$ is considered. This insight leads to a system of notions and stimulates a number of new problems. Some logical invariants of algebras $H\in\Theta$ are introduced and logical relations between different $H_1$ and $H_2$ in $\Theta$ are analyzed. The paper contains a brief review of ideas of logical geometry (§ 1), the necessary material from algebraic logic (§ 2), and a deeper introduction to the subject (§ 3). Also, a list of problems is given.
Keywords: Variety of algebras, algebraic geometry, logical geometry. 
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B. Plotkin; G. Zhitomirski. Some logical invariants of algebras and logical relations between algebras. Algebra i analiz, Tome 19 (2007) no. 5, pp. 214-245. http://geodesic.mathdoc.fr/item/AA_2007_19_5_a8/

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