[FOM] Definable Sets in ZFC
dana.scott at cs.cmu.edu
Mon Sep 20 16:22:48 EDT 2010
Recall that the axiom V = OD implies the Axiom of Choice (AC).
So, if not AC, then not all sets are in OD. Let alpha be the least
ordinal with V_alpha not included in OD. Let
BAD = V_alpha - OD.
We thus have BAD as a definable set which is non-empty and has no
definable elements. Hence the name "BAD".
Prof. Dana S. Scott
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