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.
Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications suitable to topology, group theory, and other subfields.
In A Hierarchy of Turing Degrees, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers.
Blending traditional and modern research results in computability theory, A Hierarchy of Turing Degrees establishes novel directions in the field.
Автор: Antonio Montalb?n Название: Computable Structure Theory ISBN: 1108423299 ISBN-13(EAN): 9781108423298 Издательство: Cambridge Academ Рейтинг: Цена: 17424.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Computable structure theory studies the relative complexity of mathematical structures. Written by a contemporary expert, this is the first full monograph on the subject in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings the main results and techniques in the field together into a coherent framework.
Автор: raymond turner Название: Computable Models ISBN: 1849968187 ISBN-13(EAN): 9781849968188 Издательство: Springer Рейтинг: Цена: 10475.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Computational models can be found everywhere in present day science and engineering. In providing a logical framework and foundation for the specification and design of specification languages, the author uses this framework to study computable models.
Автор: Robert I. Soare Название: Recursively Enumerable Sets and Degrees ISBN: 3540666818 ISBN-13(EAN): 9783540666813 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: ..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees.
Описание: Two of the central concepts for the study of degree structures in computability theory are computably enumerable degrees and minimal degrees. This book considers how minimal weak truth table degrees interact with computably enumerable Turing degrees and obtain three main results.
Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications suitable to topology, group theory, and other subfields.
In A Hierarchy of Turing Degrees, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers.
Blending traditional and modern research results in computability theory, A Hierarchy of Turing Degrees establishes novel directions in the field.
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