FOM: Bourbaki ordered pairs

Joseph Shoenfield jrs at
Fri May 7 10:28:01 EDT 1999

     Contrary to some recent statements in fom, Bourbaki's approach
to the ordered pair is a disaster, at least for those interested in
the structure of the set-theoretic universe.   For example, the class
of sets of rank less that the first inacessible is no longer a model
of set theory, since it may not be closed under ordered pairs.
     The purpose of the Kuratowski definition of ordered pair is to
reduce the number of primitive concepts.   This is no because reduced
numbers of concepts necessarily make a better or simpler foundations.
It is because it simplifies the study of models of set theory.   This
study is an essential tool in almost all of present day set theory.

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