Seminários de Lógica Matemática

29 de Maio 2008, 17h00

THE PRIME IDEAL THEOREM DOES NOT IMPLY THE AXIOM OF CHOICE (PART II)
SALA 3.10 - IST

ANTÓNIO FERNANDES (CMAF - U LISBOA & IST - UT LISBOA)

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.

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