GÖDEL, Kurt (1906-1978). The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis. Princeton, NJ: Annals of Mathematics Studies Number 3, Princeton University Press, 1940. 8° (226 x 150mm). First separate book publication, pp. [8], 66, [6, blank]. (Minor dogearring, a couple of leaves with faint marginal staining and finger-soiling.) Original orange stiff wrappers (spine faded and rubbed, covers creased and soiled, extremities rubbed). Provenance: ALAN TURING (no sign of provenance, bequeathed to:) -- R.O. Gandy (no sign of provenance, gifted to:) -- Prof. C.E.M. Yates (inscribed 'A.M. Turing' in Yates' hand on flyleaf).

ALAN TURING'S OWN COPY OF GÖDEL'S WORK ON THE CONTINUUM-HYPOTHESIS, the third and last of Gödel's three greatest contributions to mathematics. Georg Cantor (1845-1918) first introduced the Continuum Hypothesis in 1878, advocating that there is no set whose cardinality is strictly between that of the integers and the real numbers. Cantor believed the continuum hypothesis to be true but the proof eluded him. Its importance was such that David Hilbert listed it as the first of his 23 problems in mathematics, presented in 1900 at the Paris conference of the International Congress of Mathematicians. With the discovery of the Russell paradox, existing set theory was realized to be too naïve. An axiom system subsequently suggested by Ernst Zermelo and Abraham Fraenkel is now commonly accepted. While at Princeton between 1938-1939, 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. In other words, the Continuum Hypothesis is irrefutable from the existing accepted axioms of set theory. George W. Brown took notes of these lectures, here in the form of their FIRST SEPARATE BOOK PUBLICATION.

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