Fundamentals of Set and Number Theory

Valeriy K. Zakharov, Timofey V. Rodionov

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English

De Gruyter
05 February 2018

Mathematical logic; Set theory; Number systems; Calculus & mathematical analysis

Series: De Gruyter Studies in Mathematics

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

By: Valeriy K. Zakharov, Timofey V. Rodionov
Imprint: De Gruyter
Country of Publication: Germany
Volume: 68/1
Dimensions: Height: 240mm, Width: 170mm, Spine: 25mm
Weight: 882g
ISBN: 9783110550085
ISBN 10: 3110550083
Series: De Gruyter Studies in Mathematics
Pages: 446
Publication Date: 05 February 2018
Audience: Professional and scholarly , Professional and scholarly , Undergraduate , Undergraduate
Format: Hardback
Publisher's Status: Active

Timofey V. Rodionov and Valeriy K. Zakharov, Lomonosov Moscow State University, Russia.

Reviews for Fundamentals of Set and Number Theory

This set of two volumes evinces serious scholarship, and appears to do precisely what the authors set out to do, in homage to what Hausdorff did a century ago. It is a very valuable piece of work. Michael Berg in: MAA (09.2018), https: //www.maa.org/press/maa-reviews/sets-functions-measures-volume-1-fundamentals-of-set-and-number-theory