HILBERT, David), P(aul) BERNAYS, - Grundlagen der Mathematik. 2 vol. compl. Rare 1944 Reprint

Michigan, J. W. Edwards, Ann Arbor, 1944. 2 vol. comp. Orig cloth bindings, gilt on spine (faded). 471; 498 pp. Small name stickers at first free endpapers, furthermore a set in excellent condition, taking into account its age and method of production. In the book Grundlagen Der Mathematik, Hilbert and Bernays systematically present their proof-theoretic investigations and a wide range of current results, such as Herbrand's theorems and Gödel's incompleteness theorems. Some specialized topics are also discussed, such as the development of mathematical analysis and the unsolvability of the decision problem. Hilbert changed his basic attitude towards consistency proofs only around 1903 after the discovery of the elementary contradiction of Russell and Zermelo, which convinced him that there was a deep problem. The formalism F and the numbering are required to satisfy roughly two representability conditions: primitive recursive arithmetic is ?contained in? F; and the syntactic properties and relations of F's expressions, as well as the processes that can be carried out on such expressions, are given by primitive recursive predicates and functions. Finally, it is to consider the stimulus his approach and questions provided to contemporaries outside the Hilbert school. There is no foundational enterprise with a more profound and far-reaching effect on the emergence and development of mathematical logic.

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