Fundamentals of Set and Number Theory

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

"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