Model-theoretic applications of the profinite hull functor of special groups

This work is a development of some model-theoretic aspects of the theory of Special Groups ([9]) − a first order axiomatization of the algebraic theory of quadratic forms. In [33] we constructed a functor, the profinite hull functor, P, from the category RSG of reduced special groups with SG-morphisms to the category RSGpf of profinite reduced special groups with continuous SG-morphisms. From results concerning P, we obtain here an alternative and simple proof that the class of reduced special satisfying an interesting local-global property for p.p. formulas ([27], [28]) is an elementary class in the language of special groups, axiomatizable by Horn sentences or by ∀∃-sentences, a result originally established