[FOM] Semantical entailment between theories (to H. Friedman)

[addamo@wp.pl]

-----Original Message-----
From: addamo at wp.pl [mailto:addamo at wp.pl]
Sent: Wednesday, June 04, 2003 10:27 AM
To: fom at cs.nyu.edu
Subject: Semantical entailment between theories (to H. Friedman)


I  have a question concerning an entailment relation between theories. As an
example let us take two theories: T1 - secon order arthmetic of real numbers
and T2 - first order arithmetic of natural numbers. To the T1 belongs the
axiom of continuity (CP) and to the second the axiom of induction (AI). In
which sense could we define some relation for whixh is correct to say: CP
entails AI?

Is there any known sens in which we could say that: AI reductionally entails
CP?

Best wishes
Adam Olszewski