FOM: finite axiomatization and conservative extension

[H. Enderton]

In addition to the Kleene paper that Allen Hazen gave
(the JSL review XIX 62 discusses both this paper and Craig's
paper about decidable axiomatization), another relevant paper is
  W. Craig and R. L. Vaught
  Finite axiomatizability using additional predicates
  JSL, vol. 23 (1958), pp. 289-308
for which the JSL review is XXXVI 334.  The Kleene theorem
deserves to be better known.

--Herb Enderton
  hbe at math.ucla.edu