What is the finite axiomatizability theorem of Kleene, Craig and Vaught called, and where was it published?

logic/finite.axiomatizability New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

What is the finite axiomatizability theorem of Kleene, Craig and Vaught
called, and where was it published?

[ Editor: problem statement reconstructed from the reply; the original
question was not collected. ]

Show solution

The result is called the Kleene-Craig-Vaught finite axiomatizability
theorem.  Kleene proved the result using proof theory, later Craig and
Vaught gave a model theoretic argument, which appears in the J.S.L.
sometime around the mid 50's.  Kleene's paper appears as one of the
first memoirs of the A.M.S. in 1952.  Sorry I can't be more precise.

-- Ian Mason