[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

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