In ZF, AC implies the ultrafilter theorem (every Boolean algebra has a free ultrafilter).(adsbygoogle = window.adsbygoogle || []).push({});

- Is the converse known to be false? That is, is there a model of ZF where the ultrafilter theorem is true and AC is false?
- Does some weaker version of AC (countable choice, for example) imply the ultrafilter theorem?
- Does the ultrafilter theorem imply countable or dependent choice?
- In particular, how much choice is needed to build nonstandard analysis? Can it be done with less than AC?

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# How much choice for free ultrafilters?

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