Walter Carnielli
University of Campinas
This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".
Keywords Computable functions   Logic, Symbolic and mathematical
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ISBN(s) 0534103561   098155072X
DOI 10.2307/2687742
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On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.

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