Kenneth Kunen in his “The Foundations of Mathematics” writes: -
‘Set theory is the study of models of ZFC’ (p. 7) - ‘Set theory
is the theory of everything’ (p. 14) With (1) Kunen is pointing
to a change in the intended use of the axioms of ZFC: ‘there are
two different uses of the word “axioms”: as “statements of
faith” and as “definitional axioms”.’ (p. 6). With (2) he means
‘set theory is all-important. That is - All abstract
mathematical concepts are set-theoretic. - All concrete
mathematical objects are specific sets.’ (p. 14) According to
(1), to be a set is to be any of the individuals of the universe
of a particular model of ZFC, just like being a numeral
(standard or not) is being any of the individuals of the
universe of a particular model of PA (here I am using
Shoenfield’s terminology in “Mathematical Logic”, p. 18). But,
according to (2), models are sets too, as any other objects
dealt with in the metatheory. What's more, models of set theory
are defined in terms of relative interpretations of se