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

[Harvey Friedman]

Reply to Olszewski 11:04PM 6/4/03

>
>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?
>

In order to say what the relationship is between two theories, we 
need to have a precise formulation of the two theories.

Harvey Friedman