[FOM] Formalization Thesis
John Baldwin
jbaldwin at uic.edu
Fri Dec 28 22:40:43 EST 2007
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
312-413-2149
Room 327 Science and Engineering Offices (SEO)
851 S. Morgan
Chicago, IL 60607
Assistant to the director
Jan Nekola: 312-413-3750
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