KLEENE, S. C. [STEPHEN COLE].

On Notation for Ordinal Numbers.

Wisconsin, The Association for Symbolic Logic, 1938-39. Lev8vo. Bound in red half cloth with gilt lettering to spine. In "Journal of Symbolic Logic", Volume 3 & 4 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. A very fine copy. [Kleene:] Pp. 150-55. [Entire volume: 4, 212, (4), 194, (2) 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.: 48377