Book:Paul Isaac Bernays/Axiomatic Set Theory

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Paul Isaac Bernays: Axiomatic Set Theory

Published $1958$.

Subject Matter

Axiomatic Set Theory


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