Proof that any filter can be extended to an ultrafilter

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ultrafilter	filter	Agh! The rumors of the Daystar are true!	Tychonoff Theorem
Example of an ultraproduct	ultraproduct	Arrow's Impossibility Theorem	Ultra Bra
Optimus Prime, Ultra Magnus, and Their Forbidden Love	Ultra Obscene	principal ultrafilter	poset
cofinite filter	Captain Ultra	Ultra Fractal	Ultravision
Mathematical Induction	Service Before Self	zornification	model theory
Maximal	abstract nonsense

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