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We investigate the strength of the Ultrafilter Lemma in comparison to the Axiom of Choice. In particular, we prove that a number of classical mathematical theorems are equivalent to the Ultrafilter Lemma over $\sf ZF$, and we study a few results which are typically only obtained in $\sf ZFC$ (as opposed to $\sf ZF$) but which can also be proven from the conjunction of $\sf ZF$ with the Ultrafilter
