FOM: Re: Insall's Set Theory
Matt Insall
montez at rollanet.org
Sun Sep 24 22:36:09 EDT 2000
Prof. Shavrukov:
This seems a little bit too radical to me. By considering id : V -> V,
you would get that V is a set.
Matt:
Sorry, I should have said SET of sets. You are absolutely right.
Prof. Shavrukov:
This denies choice from class many sets, and appears to be in direct
contradiction with your GCS axiom
Matt:
You are right. I shall need to review our exchanges and your original
question to see if this malady may be corrected. In the meantime, the
following modification seems like a possibility, because it forces x to be
a
COLLECTION of classes. This collection may be a collection of class many
classes. I seem to recall that that is one way you described what you
wanted, when you called it ``local'' choice.
NLCC (revised):
(thereis x)[(forall w){[w in x] implies [w is a class]} & {(forall f)[f is
a
function] implies (thereis
y){(thereis z)[z is in y] & [y is in x] & [f(y) is not in y]}]}
[PS: Boy! I sure wish I took more time working out the details on this
one
before my first post. :)]
Dr. Matt Insall
http://www.umr.edu/~insall
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