ProofWiki:Books/Paul Isaac Bernays/Axiomatic Set Theory

Paul Isaac Bernays: Axiomatic Set Theory

Published 1958.

ISBN 0-486-66637-9

Subject Matter

Axiomatic Set Theory

Contents

Historical introduction by Abraham Fraenkel:

Introductory Remarks

Zermelo's System. Equality and Extensionality

"Constructive" Axioms of "General" Set Theory

The Axiom of Choice

Axioms of Infinity and Restriction

Development of Set-Theory from the Axioms of Z

Remarks on the Axiom Systems of von Neumann, Bernays, Gödel

Axiomatic Set Theory

The Frame of Logic and Class Theory

The Start of General Set Theory

Ordinals; Natural Numbers; Finite Sets

Transfinite Recursion

Power; Order; Wellorder

The Completing Axioms

Analysis; Cardinal Arithmetic; Abstract Theories

Further Strengthening of the Axiom System