As it is well known, some problems of algebraic geometry can be translated into problems of pure algebra (by using the polynomials). But the polynomials also provide a primitive logic which describes structural features. The aim of this paper is to study constructible sets and the foundations of algebraic geometry from the point of view of the associated mechanisms of logic. In particular, the author gets new proofs of the following results: (1) Nullstellensatz, (2) Chevalley theorem about constructible sets, (3) Absolute irreducibility of an irreducible algebraic variety defined over an algebraically closed field, (4) Existence of the unique normal finite splitting extension of a variety into degree 1 subvarieties, etc.