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Collected works of A. M. Turing. Mathematical logic. Edited by R. O. Gandy and C. E. M. Yates. Including prefaces by Solomon Feferman. (English) Zbl 0986.01023
Amsterdam: Elsevier. xii, 293 p. (2001).
Classic papers and previously unpublished writings, supplemented by expert commentary. Naturally, this volume features Turing’s 1936-7 papers in which he introduced the theoretical machine that came to bear his name and demonstrated the equivalence of the notions of Turing-computable, $$\lambda$$-definable, and (general) recursive. Also included are his 1938 paper on ordinal logics and his papers from the forties on type theory. In addition to such items, many of which have previously been anthologized elsewhere, the book contains excerpts from unpublished manuscripts, such as The Reform of Mathematical Notation and Phraseology. Also reproduced are passages from Turing’s detailed Enigma report, held secret by the United States government until 1996.
Robin Gandy, Solomon Feferman, Andrew Hodges, and others have provided thorough historical and mathematical commentary on the papers in this volume.

##### MSC:
 01A75 Collected or selected works; reprintings or translations of classics 03-03 History of mathematical logic and foundations
##### Keywords:
Alan Turing; computability; type theory; ordinal logics; Enigma