Set theory from Cantor to Cohen

Abstract

Set theory has dutifully performed the tasks that its founder Georg Cantor intended it to do and many more than Cantor could even dream of. In the present historical survey we have tried to trace some of the ideas and problems that were developed. Considering the scope of the lectures we had to restrict our attention to a modest part of set theory. We have choosen to follow set theory from Cantor via Zermelo, Fraenkel, Von Neumann, Godel to Cohen and we hoped in this way to be faithful to the spirit of Cantor. As a consequence many subjects had to be excluded, among them other variants of axiomatic set theory (e.g. Quine’s systems), the theory of types, topology, descriptive set theory (projective sets, etc.), hierarchy theory and many other subjects. Owing to the explosion in axiomatic set theory, following Cohen’s fundamental papers, we could only superficially touch the recent results. A reader interested in these new methods and results should turn to literature.