The classic results obtained by Godel, Tarski, Kleene, and Church
in the early thirties are the finest flowers of symbolic logic.
They are of fundamental importance to those investigations of the
foundations of mathematics via the concept of a formal system that
were inaugurated by Frege, and of obvious significance to the
mathematical disciplines, such as computability theory, that
developed from them.
Derived from courses taught by the author over several years, this
new exposition presents all of the results with their original
proofs and central concepts in a manner that is unified by a
systematic grounding of the notion of effectiveness in the
semantics of the existential quantifier. Logicians and
non-mathematicians, repelled by detail which is not obviously
relevant in the standard textbooks, will be able to reach the heart
of the matter with a minimum of fuss.
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