Abstract:
Let $\Theta$ be an arbitrary variety of algebras and $H$ be an algebra in $\Theta$. Along with algebraic geometry in $\Theta$ over the distinguished algebra $H$ we consider logical geometry in $\Theta$ 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 $\Theta$ algebras and consider it in the frames of logically-geometrical relations between different $H_1$ and $H_2$ in $\Theta$. The paper is aimed to give a flavor of a rather new subject in a short and concentrated manner.
Keywords and phrases:Variety of algebras, free algebra, algebraic (logical) geometry in variety, geometrically (logically) equivalent algebras.