Sets, Functions, Measures. / Volume 1, : Fundamentals of Set and Number Theory / / Timofey V. Rodionov, Valeriy K. Zakharov.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1
• VerfasserIn: Zakharov, Valeriy K.,; Rodionov, Timofey V.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2018]; ©2018
• Year of Publication: 2018
• Language: English
• Series: De Gruyter Studies in Mathematics , 68/1
• Physical Description: 1 online resource (XVIII, 428 p.)

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

Table of Contents

Frontmatter -- Contents -- Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory -- Preface -- 1 Fundamentals of the theory of classes, sets, and numbers -- A Characterization of all natural models of Neumann – Bernays – Gödel and Zermelo – Fraenkel set theories -- B Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory -- C Compactness theorem for generalized second-order language -- Index of terms -- Index of notations -- Bibliography