@MISC{WELLORD2.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Zermelo Theorem and Axiom of Choice},
  SUBTITLE = {The correspondence of well ordering relations
and ordinal numbers},
  DAY = {26},
  MONTH = {June},
  YEAR = {1989},
  ADDRESS1 = {Warsaw University\\Bia{\l}ystok},
  SUMMARY = {The article is continuation of \cite{WELLORD1.ABS} and \cite{ORDINAL1.ABS},
and the goal of it is show that Zermelo theorem (every set has a relation
which well orders it - proposition (26)) and axiom of choice (for every
non-empty family of non-empty and separate sets there is set which has
exactly one common element with arbitrary family member - proposition (27))
are true. It is result of the Tarski's axiom A introduced in \cite{TARSKI:1}
and repeated in \cite{TARSKI.ABS}. Inclusion as a settheoretical binary relation
is introduced, the correspondence of well ordering relations
to ordinal numbers is shown, and basic properties of
equinumerosity are presented. Some facts are based on \cite{KURAT-MOST:1}.}}

