  Axiomatic set theory is almost universally accepted as the basic theory which
provides the foundations of mathematics, and in which the whole of present day
mathematics can be developed. As such, it is the most natural framework for
Mathematical Knowledge Management. However, in order to be used for this task
it is necessary to overcome serious gaps that exist between the "official"
formulations of set theory (as given e.g. by formal set theory ZF) and actual
mathematical practice.
  In this work we present a new unified framework for formalizations of
axiomatic set theories of different strength, from rudimentary set theory to
full ZF. It allows the use of set terms, but provides a static check of their
validity.
