North Holland (1952)

Abstract
Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education."
Keywords Metamathematics
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Reprint years 1980, 2009
Buy this book $39.95 new   Amazon page
Call number QA9.K65
ISBN(s) 0923891579   1258442469   1258437961   0444100881   9780923891572
DOI 10.2307/2268620
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Vagueness, Truth and Logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Anti-Exceptionalism About Logic.Ole Thomassen Hjortland - 2017 - Philosophical Studies 174 (3):631-658.
Semantical Analysis of Weak Kleene Logics.Roberto Ciuni & Massimiliano Carrara - 2019 - Journal of Applied Non-Classical Logics 29 (1):1-36.

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