Re: interpolation theorem of propositional logic

Hi

David C. Ullrich wrote:
First, and more to the point: _If_ we do that
we arrive at a situation where the statement
I made that you disputed is obviously correct:
Say P and Q are unary predicates. Let alpha be
P -> P and let beta be Q -> Q. Then alpha |- beta, although there does not exist
a gamma including only sentence symbols common
to alpha and beta.

Why don't you like my gamme=false, or
alternatively gamme=true. That I suggested
in my initial post?

True and false are not 0-ary predicate symbols
or propositional variables. They are 0-ary
connectives with the following truth values:

true false
---- -----
1 0

Ok, if you use a logic without any of these
two connectives you have to use p v ~p for
true. But this is only a slight relativation
of the interpolation theorem, which I think
assumes true and/or false in the logical language.

Bye
.

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