Set theory -- from Cantor's heaven to the first theory among equals
Addressing a wider audience the author describes the development of set theory and of its logical foundations as a sequence of catastrophes (such as paradoxes, theorems of Löwenheim-Skolem, Gödel) and of attempted rescues. The nature of formal definitions and their role in the foundations of mathematics are considered in some detail. The goal of the paper is to explain how it is possible that set theory as a universal ontology of mathematics failed but the language of sets is successful in mathematical practice.
scientific article; zbMATH DE number 1249141