Boolean Valued Analysis : Mathematics and its Applications - Anatoly G. Kusraev

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Boolean Valued Analysis

By: Anatoly G. Kusraev, Semen S. Kutateladze

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348 Pages

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23.0 x 15.88 x 2.54

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Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking new tools, and for model theorists in search of challenging applications of nonstandard models.

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Foreword to the English Translation
Preface
Universes of Sets	p. 1
Boolean Valued Universes	p. 41
Functors of Boolean Valued Analysis	p. 89
Boolean Valued Analysis of Algebraic Systems	p. 141
Boolean Valued Analysis of Banach Spaces	p. 199
Boolean Valued Analysis of Banach Algebras	p. 251
Appendix	p. 281
References	p. 300
Subject Index	p. 314
Table of Contents provided by Blackwell. All Rights Reserved.

Boolean Valued Analysis

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