[FOM] Proof Theory Query
Thomas Forster
T.Forster at dpmms.cam.ac.uk
Sat Oct 10 23:19:35 EDT 2009
I am told that they are both called the *strong existence property*
Your P1 is the version appropriate for constructive theories, and P2 the
version for classical theories. Typically a constructive theory
satisfying P2 will satisfy P1 but this is not true for classical theories.
tf
On Sat, 10 Oct 2009 joeshipman at aol.com wrote:
> Let T be a recursively axiomatizable first-order theory in a language
> with countably infinitely many constant symbols c0, c1, ....
>
> Consider the following properties:
>
> P1: Whenever ExPhi(x) is in T, there exists i such that Phi(c_i) is in
> T.
>
> P2: Whenever AxPhi(x)-->Psi is in T, there exist finitely many
> constants c_i1, c_i2, ..., c_i_n such that
> ((Phi(c_i1)&Phi(c_i2)&...&Phi(c_i_n))-->Psi) is in T.
>
> What are these properties called, and can a theory have one but not the
> other?
>
> -- JS
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>
--
URL: www.dpmms.cam.ac.uk/~tf;
DPMMS ph: +44-1223-337981;
UEA ph: +44-1603-592719
Cant'y office fone: +64-3-3642987 x 8152
mobile in UK +44-7887-701-562;
mobile in NZ +64-210580093.
More information about the FOM
mailing list