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
A comprehensive, in-depth presentation of the fundamental parts of mathematics This first volume covers logic, set theory and number systems in detail Of interest to graduate students and researchers in mathematics
Timofey V. Rodionov and Valeriy K. Zakharov, Lomonosov Moscow State University, Russia.
"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