>>13869676He is saying that it is basically axiomatic set theory, but he arguments are in natural language so in that sense it is naive. In my opinion Halmos's book is massively over rated. There is not enough exercises to check your understanding. And the implementation of ordinary mathematics is boring not worth half a book. Enderton does it better, that is, going from axioms to the construction of R in a couple of chapters. But most modern set theory courses don't even cover that stuff anymore. The better order is to just define ordering, go to ordinals, some axioms, then cardinals, and then modern set theory.
