Model completeness.

A sentence X in the lower predicate calculus L is said to be defined in a set K of sentences in L if all the extralogical symbols of X occur in K. K is said to be complete if every sentence X in L which is defined in K and which is consistent with K, is deducible from K. Semantically, the completeness of a set K asserts that any two models of K satisfy the same "axioms" (sentences) which can be formulated in L using only the extralogical symbols that appear in K. Thus from the fact that the set K* of axioms for the concept of an algebraically closed field of specified characteristic is complete, it follows that a sentence X in L which is satisfied by the field of complex numbers is satisfied also by all fields of characteristic zero