FOM: finite choice
Kanovei
kanovei at wminf2.math.uni-wuppertal.de
Sun Mar 1 12:49:21 EST 1998
>Date: Sun, 01 Mar 1998 08:51:47 +0000
>From: Vaughan Pratt <pratt at cs.stanford.edu>
<choice is a theorem of Z for any given
<finite sequence of nonempty sets. (But not uniformly: there is no
<single such theorem of ZF covering all finite lengths, otherwise one
<could prove that the reals can be well-ordered.)
Finite choice is a "single theorem" of ZF and Z,
easily provable by induction on the number of
the non-empty sets considered. See any relevant
textbook.
Vladimir Kanovei
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