- #1

Fredrik

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Science Advisor

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The AC gives us permission to construct certain sets from other sets. This suggests that it makes the set-theoretic "universe"

*bigger*.

On the other hand, it's equivalent to Zorn's lemma, which implies things like "every vector space has a basis", so it seems that the AC is what ensures that certain annoying sets (like vector spaces that don't have a basis) are

*not*included in the set-theoretic universe. This seems to suggest that the AC makes the set-theoretic universe

*smaller*, not bigger.