[FOM] Truth definitions
Aatu Koskensilta
Aatu.Koskensilta at uta.fi
Wed Sep 9 10:02:21 EDT 2009
Quoting T.Forster at dpmms.cam.ac.uk:
> I promised one of my Ph.D. students that i would write out a tutorial on
> truth-definitions for him. One example it would be nice to work through is
> a consistency proof of ZF in the impredicative class theory commonly known
> as Morse-Kelley. It occurs to me that an idea that good must have been had
> before, and that there must be an elementary treatment in the literature
> somewhere. Can listmembers point me at one?
I'm pretty sure Torkel Franzén's _Inexhaustibility_ contains (at least
a sketch or a brief account of) such a proof, though probably in an
arithmetic context (i.e. for PA in second-order arithmetic). The only
technical subtlety to the proof I can think of is that the usual
deductive systems allow open formulas in deductions, which one takes
care of either by using a satisfaction predicate or by including a
constant for every set in the language.
--
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
More information about the FOM
mailing list