  This is an expository paper in which I explain how core mathematics,
particularly abstract analysis, can be developed within a concrete countable
set J_2 (the second set in Jensen's constructible hierarchy). The implication,
well-known to proof theorists but probably not to most mainstream
mathematicians, is that ordinary mathematical practice does not require an
enigmatic metaphysical universe of sets. I go further and argue that J_2 is a
superior setting for normal mathematics because it is free of irrelevant
set-theoretic pathologies and permits stronger formulations of existence
results.
