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Aatu Koskensilta says...
>Quite so. In fact set theoretical truth is definable in NBG: there is a
>formula True(x) such that NBG proves for every formula A that True('A')
><--> A. NBG does not prove all the usual clauses in the usual inductive
>definition for truth, however. I gave an axiomatization of NBG based on
>this observation some time ago here in sci.logic.
>
>And of course, from the observation that ZFC* is acceptable on basis of
>our picture of the world of sets, we see that ZFC** with a second truth
>predicate covering also formulas involving the truth predicate of ZFC*
>is also acceptable, and similarly for ZFC*** and so forth.
How do this sequence of theories fit in with Morse-Kelly set theory?
I'm pretty sure that ZFC* is still a subtheory of MK, but I'm not
sure about ZFC**.
--
Daryl McCullough
Ithaca, NY
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