[FOM] Proof Theory Query
joeshipman at aol.com
Sat Oct 10 10:57:47 EDT 2009
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
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