[FOM] Dependent Choice and Ultrafilters

D.R. MacIver drm39 at cam.ac.uk
Tue Mar 22 05:22:15 EST 2005

Does anyone happen to know if ZF + DC(omega) + `Every filter on a set is 
contained in an ultrafilter' implies DC(omega_1)? I can't imagine that it 
does, but I also can't find any references for it (and my knowledge of 
forcing is still rather theoretical and extremely weak, so I can't manage 
much in the way of an independence proof myself).


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