TURING, Alan Mathison (1912-1954). 'Systems of logic based on ordinals.' Offprint from: Proceedings of the London Mathematical Society, ser. 2, vol. 45. London: 1939. 8° (256 x 176mm). 68pp., 161-228. Original olive-green wrappers, stapled (nick to spine, rear wrapper starting to split). Provenance: ALAN TURING (correction to footnote on p.181 possibly in the author's hand; bequeathed to:) -- R.O. Gandy (no sign of provenance).

OFFPRINT OF TURING'S DOCTORAL DISSERTATION, in which he investigates ordinal logics and Gödel's theorem. 'This introduced the idea of relative computability, or relative unsolvability, which opened up a new field in mathematical logic' (Hodges, p.143). Newman 1939.

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