Re: FO logic without equality

On Sat, 03 Jun 2006 13:10:44 +0200, Jan Burse <janburse@xxxxxxxxxxx>
wrote:



David C. Ullrich wrote:

Exactly what part of that pdf do you think says that
it doesn't matter? That it doesn't matter _to_ _this_
_question_, not that it doesn't matter for some
_other_ purpose.

The papers say:

S u EQ_AX satisfiable iff S normal satisifiable

From this follows what I said:

T u EQ_AX |- A iff T |-_= A

What you said was that whether we're talking about
FOL with or without equality does not matter to
whether it is true that if T has a model then
T has an infinite model. How does _that_ follow
from the above?

Proof:

By (normal) completness:
S u EQ_AX satisfiable <=>
S u EQ_AX consistent <=>
S normal satisfiable <=>
S normal consistent

Further
T u EQ_AX |- A <=>
T u EQ_AX u ~A not consistent <=>
T u ~A not normal consistent <=>
T |-_= A

Bye


************************

David C. Ullrich
.

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