Generalized Recursion Theory

Generalized Recursion Theory
Author: Lev D. Beklemishev
Publisher: Elsevier
Total Pages: 465
Release: 2000-04-01
Genre: Computers
ISBN: 0080954898
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Generalized Recursion Theory

Admissible Sets and Structures

Admissible Sets and Structures
Author: Jon Barwise
Publisher: Cambridge University Press
Total Pages: 409
Release: 2017-03-02
Genre: Mathematics
ISBN: 1107168333
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This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.

Computability and Complexity

Computability and Complexity
Author: Adam Day
Publisher: Springer
Total Pages: 788
Release: 2016-11-30
Genre: Computers
ISBN: 3319500627
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This Festschrift is published in honor of Rodney G. Downey, eminent logician and computer scientist, surfer and Scottish country dancer, on the occasion of his 60th birthday. The Festschrift contains papers and laudations that showcase the broad and important scientific, leadership and mentoring contributions made by Rod during his distinguished career. The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence. The volume contains several surveys that make the various areas accessible to non-specialists while also including some proofs that illustrate the flavor of the fields.

Classical Recursion Theory

Classical Recursion Theory
Author: P. Odifreddi
Publisher: Elsevier
Total Pages: 667
Release: 1992-02-04
Genre: Computers
ISBN: 9780080886596
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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.

Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles

Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles
Author: Denis R Hirschfeldt
Publisher: World Scientific
Total Pages: 231
Release: 2014-07-18
Genre: Mathematics
ISBN: 9814612634
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This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.

Harvey Friedman's Research on the Foundations of Mathematics

Harvey Friedman's Research on the Foundations of Mathematics
Author: L.A. Harrington
Publisher: Elsevier
Total Pages: 407
Release: 1985-11-01
Genre: Mathematics
ISBN: 9780080960401
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This volume discusses various aspects of Harvey Friedman's research in the foundations of mathematics over the past fifteen years. It should appeal to a wide audience of mathematicians, computer scientists, and mathematically oriented philosophers.

The Higher Infinite

The Higher Infinite
Author: Akihiro Kanamori
Publisher: Springer Science & Business Media
Total Pages: 555
Release: 2008-11-23
Genre: Mathematics
ISBN: 3540888675
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Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

Interpolation and Definability

Interpolation and Definability
Author: Dov M. Gabbay
Publisher: Oxford University Press
Total Pages: 524
Release: 2005-05-12
Genre: Computers
ISBN: 0198511744
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This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and NonmonotonicReasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.

Higher Set Theory

Higher Set Theory
Author: G.H. Müller
Publisher: Springer
Total Pages: 481
Release: 2007-01-05
Genre: Mathematics
ISBN: 3540357491
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