The principle of moduli flexibility for real algebraic manifolds

Given a real closed field R, we define a real algebraic manifold as an irreducible nonsingular algebraic subset of some R^n. This paper deals with deformations of real algebraic manifolds. The main purpose is to prove rigorously the reasonableness of the following principle, which is in sharp contrast with the compact complex case: "The algebraic structure of every real algebraic manifold of positive dimension can be deformed by an arbitrarily large number of effective parameters".