First-Order Axiom Systems

Abstract

In order to keep this book to a reasonable size we have decided not to give an extensive treatment of subjects that can be found elsewhere and that are somewhat peripheral to our primary interests. That policy begins to have an effect now. Proving completeness of first-order axiomatizations can be quite complex—see (Garson, 1984) for a full discussion of the issues involved. Indeed, a common completeness proof that can cover constant domains, varying domains, and models meeting other conditions, does not seem available, so a thorough treatment would have to cover things separately for each version. Instead we simply present some appropriate axiomatizations, make a few pertinent remarks, and provide references. For machinery presented in later chapters we omit an axiomatic treatment altogether.