Denis R. Hirschfeldt's Books

Algorithmic Randomness and Complexity

By: Rodney G. Downey,Denis R. Hirschfeldt

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Algorithmic Randomness and Complexity

By: Rodney G. Downey,Denis R. Hirschfeldt

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

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Page Count

883

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387684417

ISBN 13

9780387684413

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

By: Denis R Hirschfeldt

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

By: Denis R Hirschfeldt

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.

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Page Count

231

Publisher

World Scientific

Published Date

ISBN 10

9814612634

ISBN 13

9789814612630

Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem

By: Denis R. Hirschfeldt,Karen Lange,Richard A. Shore

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Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem

By: Denis R. Hirschfeldt,Karen Lange,Richard A. Shore

Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.

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Page Count

114

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470426579

ISBN 13

9781470426576

Book's by Denis R. Hirschfeldt

Algorithmic Randomness and Complexity

Algorithmic Randomness and Complexity

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

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

Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem

Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem

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