@MISC{ZFMODEL1.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Properties of {ZF} Models},
  DAY = {05},
  MONTH = {July},
  YEAR = {1989},
  ADDRESS1 = {Warsaw University\\Bia{\l}ystok},
  SUMMARY = {  The article deals with the concepts of satisfiability of ZF set theory
language formulae in a model (a non-empty family of sets) and the axioms of
ZF theory introduced in \cite{MOST:1}. It is shown that
the transitive model satisfies the axiom of extensionality and that
it satisfies the axiom of pairs if and only if it is closed to pair
operation; it satisfies the axiom of unions if and only if it is closed
to union operation, etc. The conditions which are satisfied by arbitrary
model of ZF set theory are also shown.
Besides introduced are definable and parametrically definable
functions.}}

