[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.


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
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