Elimination of quantifiers of a theory of real closed rings.

Abstract

Let T* be the theory of lattice-ordered subrings, without minimal (non zero) idempontents, convex in von Neumann regular real closed rings that are divisible-proyectable and sc-regular. In this paper, a local divisibility binary relation is introduced in order to prove the elimination of quantifiers of the theory T* in the language of lattice-ordered rings adding the divisibility relation, the radical relation associated to the minimal prime spectrum and this new local divisibility relation.