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Let Θ be an arbitrary variety of algebras and H an algebra in Θ. Along with algebraic geometry in Θ over the distinguished algebra H, a logical geometry in Θ 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 ∈ Θ are introduced and logical relations between different H1 and H2 in Θ 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. 0.

Some logical invariants of algebras and logical relations between algebras