Re: Proper classes


Without global choice you can have incomparable proper classes, as can be seen rather trivially: take a model of ZFC in which there is no definable well-ordering of V and add on top of it the definable subsets as classes and you'll have a model of NBG in which there is no bijection between V and the class of ordinals.

This doesn't establish the consistency of having incomparable proper classes, of course, only of proper classes not equipollent with each other. That's what you get when posting in the morning prior to consuming sufficient amounts of caffeine.

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Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

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