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Published online by Cambridge University Press: 10 May 2010
Before we list the axioms of set theory, we make one more important remark. The fact that in the language we have the only predicate symbols = and ∈, and we do not introduce a one-place predicate symbol to say that something is a set implicitly means that we only discuss sets; other objects are of no concern to us. The attentive reader may have noticed that this practice was tacitly followed even in the first part of the book, after the introduction of good sets. That this will not impose undue restrictions on us will be clear exactly from the fact that the axiomatic development can be carried out in this way.
The today generally accepted Zermelo–Fraenkel axiom system of set theory contains the following axioms.
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