About existence-as-consistency

[Vaughan Pratt]

Giovanni Sambin began by raising what sounded like a perfectly conventional
and reasonable question of history: who said what when before the time it
became well known that a first order theory was consistent iff it had a
model?

But then he asked "is there a way to avoid assuming EaC while keeping
classical logic (and hence validity of LEM)?"

The "is" suggests that this is no longer an historical question.

Consistence of a first order theory T is well-defined, but what about
existence?

One definition would be that an interpretation of the language of T exists
if and only if it is a model of T.

With that definition, the answer to Giovanni's question would appear to be
"No".

What definition of "existence" would admit a positive answer?

Vaughan Pratt
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