[FOM] Definable Sets in ZFC

Dana Scott 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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