[FOM] Proof Theory Query
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.
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
> 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
> -- JS
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