  The main objective of this paper is to show that the notion of type which was
developed within the frames of logic and model theory has deep ties with
geometric properties of algebras. These ties go back and forth from universal
algebraic geometry to the model theory through the machinery of algebraic
logic. We show that types appear naturally as logical kernels in the Galois
correspondence between filters in the Halmos algebra of first order formulas
with equalities and elementary sets in the corresponding affine space.
