For ten points, identify this controversial statement in set theory stating that the Cartesian product of nonempty sets is nonempty, which makes up the C in ZFC.
Erret Bishop argued that this statement is constructively acceptable because its namesake concept is implied by the meaning of existence. This statement implies Krull's theorem and ensures that every partially ordered set has a maxi- mal antichain. This statement implies that every vector space has a   basis and that every product of compact spaces is compact. This statement is equivalent to the statement that every set has a well-ordering, as well as Zorn's lemma. For ten points, identify this controversial statement in set theory stating that the Cartesian product of nonempty sets is nonempty, which makes up the C in ZFC.
Erret Bishop argued that this statement is constructively acceptable because its namesake concept is implied by the meaning of existence.
axiom of choice [prompt on anything equivalent to the Axiom of Choice like Zorn's lemma and well-ordering principle, unless it's already been        read (because the  rst clue is unique to AC)]