Systems of Logic Based on Ordinals IN: Proceedings of the London Mathematical Society First Edition - A.M. Turing - Bauman Rare Books

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Systems of Logic Based on Ordinals IN: Proceedings of the London Mathematical Society

A.M. TURING

Item#: 110032 We're sorry, this item has been sold

Systems of Logic Based on Ordinals IN: Proceedings of the London Mathematical Society

Systems of Logic Based on Ordinals IN: Proceedings of the London Mathematical Society

Systems of Logic Based on Ordinals IN: Proceedings of the London Mathematical Society

EXCEPTIONAL FIRST PUBLICATION OF TURING'S GROUND-BREAKING DOCTORAL THESIS ON LOGIC

TURING, A.M. "Systems of Logic Based on Ordinals." IN: Proceedings of The London Mathematical Society, Second Series, Volume 45, pp. 161-228. London: C.F. Hodgson & Son, 1939. Large octavo, modern red cloth. Housed in a custom clamshell box.

First publication of Turing's critically important PhD thesis presenting the possibility of avoiding Gödel's incompleteness theorem by introducing systems of logic obtained from one another by transfinite iteration.

Written between 1937 and 1938 at Princeton under the supervision of Alonzo Church, Turing's PhD thesis focused on systems of logic based on ordinals. As Turing's advisor, Alonzo Church influenced the thesis heavily. On May 7, 1938, Turing wrote to his sister, "Church made a number of suggestions which resulted in the thesis being expanded to an appalling length. The thesis has just been accepted today" (Copeland, 134). The thesis explored the possibility of avoiding Gödel's incompleteness theorem by introducing systems of logic obtained by transfinite iteration (Davis, 154). Turing examined the question of constructing to any ordinal number "alpha" a logic Lalpha, so that problems could be solved within Lalpha. Also, Turing introduced the idea of an "oracle," which was not a machine in itself, but which could be used to form machines (o-machines) "having as one of [their] fundamental processes that of solving a given number-theoretic problem" (page 173). The influence of the paper proved far-reaching, in logic, computing, and beyond. Also in this volume is John Henry Constantine Whitehead's "Simplicial Spaces, Nuclei and M-Groups," pp. 243-327, considered to be his most significant work.

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Aquatint Copperplate process by which the plate is “bitten” by exposure to acid. By changing the areas of the plate that are exposed and the length of time the plate is submerged in the acid bath, the engraver can obtain fine and varying shades of gray that closely resemble watercolor washes. Although the name contains the word “tint”, this is a black-and-white printing process; aquatint plates can often be hand colored, however.
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