THE CONSISTENCY OF SET THEORY

GÖDEL, KURT

The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis (+) Consistency-proof for the Generalized Continuum-Hypothesis.

Washington, 1938 & 1939. Royal8vo. 2 volumes, uniformly bound in contemporary full cloth with gilt lettering to spine. Exlibris to front paste down. In "Proceedings of the National Academy of Science", vol. 24 and 25. Fine and clean. Pp.556-57; Pp. 220-24). [Entire volumes: VII, 572 pp.; VII, 661 pp].

First edition of arguable Gödel's most important publications only second to his incompleteness theorem.
The first problem of Hilbert's famous 1900 address asks for a proof of Cantor's continuum hypothesis. Hilbert considered this problem one of the most important problems confronting the mathematical world. As a first step towards such a proof Ernst Zermelo proved in 1904 another hypothesis by Cantor, namely that every set can be well ordered. In his proof Zermelo introduced a necessary tool which later became known as the axiom of choice. Because of its non-constructive nature this axiom, and the continuum hypothesis, became the object of much controversy in the mathematical community. Gödel's results on this topic are, besides his completeness and incompleteness theorems, his most celebrated. During the autumn terms of 1938 and 1939 Gödel delivered a series of lectures at the Institute for Advanced Study, in which he proved that the axiom of choice and the generalized continuum hypothesis are consistent with the other axioms of set theory if these axioms are consistent.

Order-nr.: 58791