Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080957609
Category : Computers
Languages : en
Pages : 329

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Book Description
Formal Systems and Recursive Functions

Author: Raymond M. Smullyan
Publisher: Princeton University Press
ISBN: 1400882001
Category : Science
Languages : en
Pages : 156

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Book Description
This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.

Author: Raymond M. Smullyan
Publisher: Princeton University Press
ISBN: 9780691080475
Category : Mathematics
Languages : en
Pages : 160

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Book Description
This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.

Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 9780080957463
Category : Mathematics
Languages : en
Pages : 160

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Book Description
Provability, Computability and Reflection

Author: P. Odifreddi
Publisher: Elsevier
ISBN: 9780080886596
Category : Computers
Languages : en
Pages : 667

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Book Description
1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.

Author: Rod Adams
Publisher: Docent Press
ISBN: 0983700400
Category : Mathematics
Languages : en
Pages : 312

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Book Description
Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

Author: Roman Murawski
Publisher: Springer Science & Business Media
ISBN: 9401728666
Category : Philosophy
Languages : en
Pages : 416

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Book Description
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.

Author: Naoki Abe
Publisher: Springer
ISBN: 3540455833
Category : Computers
Languages : en
Pages : 388

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Book Description
This volume contains the papers presented at the 12th Annual Conference on Algorithmic Learning Theory (ALT 2001), which was held in Washington DC, USA, during November 25–28, 2001. The main objective of the conference is to provide an inter-disciplinary forum for the discussion of theoretical foundations of machine learning, as well as their relevance to practical applications. The conference was co-located with the Fourth International Conference on Discovery Science (DS 2001). The volume includes 21 contributed papers. These papers were selected by the program committee from 42 submissions based on clarity, signi?cance, o- ginality, and relevance to theory and practice of machine learning. Additionally, the volume contains the invited talks of ALT 2001 presented by Dana Angluin of Yale University, USA, Paul R. Cohen of the University of Massachusetts at Amherst, USA, and the joint invited talk for ALT 2001 and DS 2001 presented by Setsuo Arikawa of Kyushu University, Japan. Furthermore, this volume includes abstracts of the invited talks for DS 2001 presented by Lindley Darden and Ben Shneiderman both of the University of Maryland at College Park, USA. The complete versions of these papers are published in the DS 2001 proceedings (Lecture Notes in Arti?cial Intelligence Vol. 2226).

Author: M. Fitting
Publisher: Elsevier
ISBN: 0080960316
Category : Mathematics
Languages : en
Pages : 329

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Book Description
Fundamentals of Generalized Recursion Theory

Author: Geoffrey Hunter
Publisher: Univ of California Press
ISBN: 9780520023567
Category : Mathematics
Languages : en
Pages : 306

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Book Description
This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically truth-functional) first order logic. Included is a complete proof, accessible to non-mathematicians, of the undecidability of first order logic, the most important fact about logic to emerge from the work of the last half-century. Hunter explains concepts of mathematics and set theory along the way for the benefit of non-mathematicians. He also provides ample exercises with comprehensive answers.