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This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.

Nonstandard mathematical analysis --- Mathematics --- Congresses. --- Mathematical analysis --- Mathematical analysis [Nonstandard ] --- Congresses --- Mathematical analysis, Nonstandard - Congresses. --- Analysis, Nonstandard mathematical --- Mathematical analysis, Nonstandard --- Non-standard analysis --- Nonstandard analysis --- Model theory --- Nonstandard mathematical analysis - Congresses

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Pro matematiku dvacátého století je príznacné, že její hlavní proud nekonecno zkoumající a zároven aplikující, byt v bizarních ideálních svetech, je založen na klasické Cantorove teorii nekonecných množin. Ta sama se pak opírá o problematický predpoklad existence množiny všech prirozených císel, jehož jediné - a to navíc teologické - oduvodnení bývá zamlcováno a vytlacováno do kolektivního nevedomí.I když autor uvádí nekterá durazná varování znamenitých matematiku pred nebezpecími skrytými v soucasné infinitní matematice, není jím budovaná nová infinitní matematika jen pouhou negací soucasných názoru a predpokladu. Naopak, ta infinitní matematika, do níž predbežným úvodem je tento spisek, je vedena opatrnou snahou o nová prekracování obzoru ohranicujícího antický geometrický svet.

Nonstandard mathematical analysis. --- Analysis, Nonstandard mathematical --- Mathematical analysis, Nonstandard --- Non-standard analysis --- Nonstandard analysis --- Model theory

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Nonstandard mathematical analysis --- Analysis, Nonstandard mathematical --- Mathematical analysis, Nonstandard --- Non-standard analysis --- Nonstandard analysis --- Model theory --- Nonstandard mathematical analysis.

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Mathematical analysis --- Mathematical logic --- Mathematical analysis, Nonstandard --- Congresses --- 510.6 --- Nonstandard mathematical analysis --- 510.6 Mathematical logic --- Analyse mathématique non standard --- Analyse mathématique --- Analyse mathématique. --- Analyse mathématique non standard. --- Mathematical analysis, Nonstandard - Congresses --- Analyse mathématique. --- Analyse mathématique non standard.

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Provability, Computability and Reflection

Mathematical analysis --- Logic, Symbolic and mathematical --- Analyse mathématique --- Logique symbolique et mathématique --- Congresses --- Congrès --- EPUB-LIV-FT ELSEVIER-B --- Nonstandard mathematical analysis --- Analysis, Nonstandard mathematical --- Mathematical analysis, Nonstandard --- Non-standard analysis --- Nonstandard analysis --- Model theory