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Martin Väth
Martin Väth
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What is your definition of meager in (ZF)? Being a countable union of nowhere dense sets? In that case, the given argument about the failure of (UUMUMM) in (ZF) is not clear: It is not obvious (to me) that the real line cannot be be meager in (ZF). Recall that the general category theorem of Baire is in (ZF) equivalent to countable dependent choices (DC); perhaps a proof that the real line is not meager already requires more than ZF?

What is your definition of meager in (ZF)? Being a countable union of nowhere dense sets? In that case, the given argument about the failure of (UUM) in (ZF) is not clear: It is not obvious (to me) that the real line cannot be be meager in (ZF). Recall that the general category theorem of Baire is in (ZF) equivalent to countable dependent choices (DC); perhaps a proof that the real line is not meager already requires more than ZF?

What is your definition of meager in (ZF)? Being a countable union of nowhere dense sets? In that case, the given argument about the failure of (UMM) in (ZF) is not clear: It is not obvious (to me) that the real line cannot be be meager in (ZF). Recall that the general category theorem of Baire is in (ZF) equivalent to countable dependent choices (DC); perhaps a proof that the real line is not meager already requires more than ZF?

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Source Link
Martin Väth
Martin Väth
  • 1.9k
  • 1
  • 6
  • 12

What is your definition of meager in (ZF)? Being a countable union of nowhere dense sets? In that case, the given argument about the failure of (UUM) in (ZF) is not clear: It is not obvious (to me) that the real line cannot be be meager in (ZF). Recall that the general category theorem of Baire is in (ZF) equivalent to countable dependent choices (DC); perhaps a proof that the real line is not meager already requires more than ZF?