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Fundamentals of Set and Number Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov

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Fundamentals of Set and Number Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

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Page Count

448

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110550946

ISBN 13

9783110550948

Fundamentals of Functions and Measure Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

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Fundamentals of Functions and Measure Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals

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Page Count

597

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110550229

ISBN 13

9783110550221