On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Gödel, Kurt - 1962

London: Oliver & Boyd (1962), 1962. First UK edition. Hardcover. Very near Fine/Near Fine. Small 8vo. [6], vii-viii, 1-72 pp. Bound in tan cloth with brown lettering on the spine. Translated by B. Meltzer, with an introduction by R. B. Braithwaite. Kline 1206-1207. Omega Bibliography I 212. Risse II 315. Slater 345. This is the first edition in English of one of Godel's landmark works, originally published in German in 1931 as "Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme I" in the journal Monatshefte fur Mathematik und Physik. The principal result in this work is generally known as Godel's Incompleteness Theorem which is a proof that any consistent formal system S which includes the standard axioms of arithmetic (as axioms or theorems) is incomplete, that is, there is some proposition P in the system S such that neither P nor its negation is provable in S (in other words, there must be a proposition which is either true or false, but which cannot be proven in S). Kurt Gödel won the first Albert Einstein award in 1951, was awarded the National Medal of Science in 1974, and is regarded as one of the greatest and most influential mathematicians in all of history. A very nice example of Godel's second book, a milestone in the history of mathematics. Very near Fine in a Near Fine dust jacket with some minor wear to the extremities.