[FOM] A generalization of RIce`s theorem for logical theories
Richard Zach
rzach at ucalgary.ca
Mon Oct 13 17:54:17 EDT 2008
I'm curious how exactly your result goes. Surely what's undecidable is
not if a theory has property P but if some representation (e.g., a
Turing machine enumerating theorems, a finite axiom system) generates a
theory that has P?
In any event, this might be related:
M. G. Peretyat'kin. Analogues of Rice's theorem for semantic classes of
propositions. Algebra and Logic 30 (1991) 332-348
http://www.springerlink.com/content/n17678u57v124m4m/
Best,
R
On Sun, 2008-10-12 at 21:32 -0300, carniell at cle.unicamp.br wrote:
> A property P defined over the collection of all first-order
> theories is said to be "non-trivial" if it holds for some, but
> not all theories. Then any non-trivial property P is undecidable.
> Does anyone knows if a similar result is already known, or
> folklore?
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