[FOM] Formalization Thesis

[John Baldwin]

I cut from Kutateladze's reply to Chow.

On Fri, 28 Dec 2007, S. S. Kutateladze wrote:

> I explain simply that  all branches of mathematics cannot be translated
> fully neither into set theory  nor into any unique formal theory.
> Category theory yields an illustration, as well as model theory.
>
I want first to adopt Catarin's Dutilh's nice distinction between the 
expressibility thesis and the provability thesis.

Clearly for the model theory the provability thesis is false for ZFC; thre 
are plenty of published examples (e.g. existence of saturated models in 
various cardinals; the necessity of the weak GCH to prove categoricity 
transfer for L-omega_1, omega etc. etc.

But Kutaleladez seems to have a wider view of model theory than I if 
denies the expressibility thesis. To me, model theory is essentially built 
on Tarski's formal definition of truth in set theory. And to state a 
theorem in model theory is to state one that is expressible in the 
langugage of set theory.

I would like 
an example of a model theoretic proposition that is not so expressible.



John T. Baldwin
Director, Office of Mathematics Education
Department of Mathematics, Statistics, 
and Computer Science  M/C 249
jbaldwin at uic.edu
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Jan Nekola: 312-413-3750