Abstract:
The completeness theorem for coherent propositional logic, alias
the Prime Ideal Theorem (PIT) for distributive lattices, is true
in certain non-boolean toposes. But it is only strong enough to
prove the Order Extension Principle (OEP) for decidable objects.
We introduce an extension of coherent propositional logic whose
completeness theorem is stronger than (PIT). In particular, it
is strong enough to conclude (OEP) for arbitrary objects.
This is the second in a series of talks concerning the axiom of
choice for (Kuratowski-)finite sets and ``related issues''.