I've read 'Axiomatic Set Theory' by Patrick Suppes, and one thing I've noticed throughout is that he seems to be obsessed with definitions, and he tries to allow for urelements. Is this standard for ZFC?
I thought in general when we say 'set' in ZFC we really mean 'pure set', and so avoid having to worry about individuals. In addition I've never seen such a fuss over definitions in any other mathematical book I've read, is this something I should get used to in Set Theory?
If this is not standard, can anyone direct me to a book similar to Suppes' which builds (from the axioms) all the usual set theoretical structures needed for other areas of mathematics that is?
From Wikipedia:
The Zermelo set theory of 1908 included urelements. It was soon realized that in the context of this and closely related axiomatic set theories, the urelements were not needed because they can easily be modeled in a set theory without urelements. Thus standard expositions of the canonical axiomatic set theories ZF and ZFC do not mention urelements (For an exception, see Suppes).