The Axioms of Zermelo–Fraenkel Set Theory

Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In the middle and late 19th century, members of the then small mathematical community began to look for a rigorous foundation of Mathematics. In accordance with the Euclidean model for reason, the ideal foundation consists of a few simple, clear principles, so-called axioms, on which the rest of knowledge can be built via firm and reliable thoughts free of contradictions. However, at the time it was not clear what assumptions should be made and what operations should be allowed in mathematical reasoning.

After a short introduction to First-Order Logic, we shall introduce and discuss in this chapter the axioms of Zermelo–Fraenkel Set Theory.

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© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland

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