Seminários de Lógica Matemática 29 de Maio 2008, 17h00 Abstract: It is well known that using the axiom of choice (AC) we can prove that every Boolean algebra has a prime ideal, a statement known as the Prime Ideal Theorem (PIT). In its dual form PIT is the Ultrafilter Theorem which is equivalent to the principle of compactness for first-order logic. We will prove that the PIT is not strong enough to prove AC modulo the axioms of ZF set theory. | back |