Local divisibility and model completeness of a theory of real closed rings

Abstract

Let T∗ be the theory of lattice-ordered rings convex in von Neumann regular real closed f-rings, without minimal idempotents (non zero) that are divisible-projectable and sc-regular. I introduce a binary relation describing local divisibility. If this relation is added to the language of lattice ordered rings with the radical relation associated to the minimal prime spectrum (cf. [12]), it can be shown the model completeness of T∗.