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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. Contents: Setting Off: An Introduction Gathering Our Tools: Basic Concepts and Notation Finding Our Path: Kö,nig',s Lemma and Computability Gauging Our Strength: Reverse Mathematics In Defense of Disarray Achieving Consensus: Ramsey',s Theorem Preserving Our Power: Conservativity Drawing a Map: Five Diagrams Exploring Our Surroundings: The World Below RT22 Charging Ahead: Further Topics Lagniappe: A Proof of Liu',s Theorem Readership: Graduates and researchers in mathematical logic. Key Features: This book is self-contained and unified in presentation It describes the latest development in fabrication technologies, high power lasers, short pulse generation, and photonic crystal fibers It describes the latest development in applications of fiber amplifiers and fiber lasers in optical transmission, industrial systems, supercontinuum generation and fiber based sensors

Detalhes do Produto

    • Formato:  ePub
    • Origem:  IMPORTADO
    • Editora: WSPC
    • Coleção:  Lecture Notes Series, Institute for Mathematical S
    • Assunto: Medicina
    • Idioma: INGLÊS
    • Ano de Edição: 2014
    • Ano:  2014
    • País de Produção: Canada
    • Código de Barras:  2001121447642
    • ISBN:  9789814612630

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