Amalgamation and elimination of quantifiers for theories of fields
William H. Wheeler · Proceedings of the American Mathematical Society · 1979
The universal theories of integral domains and of ordered integral domains which have the amalgamation property are characterized via their existentially complete models. The results of A. Macintyre, K. McKenna, and L. van den Dries on fields and ordered fields whose complete theories permit elimination of quantifiers are then derived as easy corollaries.