[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


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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