Re: Set Theory Exercise



Max Weiss wrote:
> Dear all,
>
> I'm stuck on Exercise 4.4.3,
> in Smullyan and Fitting's _Set Theory and
> the Continuum Problem_.
>
> It says: Show that if there's
> a choice function for a set S, then
> there's a choice function for union(S).

There MUST be a hypothesis missing, as you've
stated it. I mean, here is an obvious counter-
example: let 0=the-empty-set, and x={0}.
Then let S={x}={{0}}. Precisely as you argued,
there is a choice-function for S={{0}},
namely, {<{0},0}>}. But equally clearly, there
is no choice-function for U(S)={0}, since every set in
{0} is empty.

Are we supposed to be talking about infinite sets?
That would be a reasonable restriction since every
finite set of sets is known to have exactly as
many choice-functions as the product of the cardinalities
of its members.

.

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