KLEENE, S. C. [STEPHEN COLE].

On Notation for Ordinal Numbers.

Wisconsin, The Association for Symbolic Logic, 1938-39. Lev8vo. Entire volume one of "Journal of Symbolic Logic" (i.e. number 1-4), March 1938, June 1938, October 1938, January 1939. Bound in blue half cloth with gilt lettering to spine. Crossed-out library paper-label to lower part of spine and top left corner of front board. Two library stamps (in Chinese) to verso of title page. Internally a very fine and clean copy of the entire volume. [Kleene:] Pp. 150-55. [Entire volume: IV, 212 pp.].

First printing Kleene's milestone paper in which Kleene's O (Ordial numbers), a recursive function, is introduced. In set theory and computability theory, Kleene's is a canonical subset of the natural numbers when regarded as ordinal notations.
"In the seventeenth century, Leibniz envisaged a universal language that would allow one to reduce mathematical proofs to simple computations. Then, during the nineteenth century, llgicians such as Charles Babbage, Boole, Frege and Peano tried to formalize mathematical reasoning by an "algebraization" of logic. Finally, [...] Gödel, Church and Stephen Kleene introduced the notion of recursive functions. (The Princeston Companion to Mathematics. P. 111).

The volume also contains the following papers of interest:
1. Quine, W. V. Completeness of the propositional calculus. Pp. 37-40
2. Quine, W. V. On the theory of types. Pp. 125-39.
3. Church, Alonzo. Additions and corrections to A bibliography of symbolic logic. Pp. 178-92.

Order-nr.: 44273