[FOM] Explanation/Continuum Hypothesis

Bill Taylor W.Taylor at math.canterbury.ac.nz
Sun May 7 02:15:45 EDT 2006

Alasdair Urquhart <urquhart at cs.toronto.edu> suggests:

->Kurt Goedel made some remarks about this, which were roughly as follows.
->The axioms of set theory are satisfied for two quite different conceptions
->of set, namely the notion of a definable collection (the constructible
->sets) and also the notion of a random totality of objects --
->a generic set can be considered as a random totality in this sense.

Are you intending to except AC from the first case (definable collection)?
If not, how is it clear that AC holds for this?

->The continuum hypothesis is valid on the first conception but not
->the second.

Though as I noted here before, CH can be reworded in two ways,
equivalent under AC but not otherwise, one of which is true
and one false in the "definable" interpretation. Though the "obvious"
interpretation is true, as you say.

Bill Taylor

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