[FOM] The liar and the semantics of set theory

[praatika@mappi.helsinki.fi]

Roger Bishop Jones <rbj at rbjones.com> wrote:

> The liar "paradox" was used by Tarski to show that
> arithmetic truth is not definable in arithmetic.
> 
> It is natural to suppose that a similar result obtains in
> relation to set theory, viz. that set theoretic truth is not
> definable in set theory.
> However, I am not aware of any argument (using the
> liar or otherwise) which conclusively demonjstrates
> this conjecture.

RE: I am. And quite obviously, the generalized Goedel-Tarski trick applies 
to any recursively axiomatizable theory which contain Robinson Arithmetic. 
But if you want a direct application to the language of ZFC, see e.g. 

K. Kunen: Set theory, §14 8p. 38.42)
K. Doets: Basic model theory, p. 7-9.

Cheers

Panu Raatikainen