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Topic: Some Questions about Infinite Sets
Replies: 3   Last Post: May 12, 2011 11:18 AM

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Posts: 2,394
Registered: 8/3/07
Re: Some Questions about Infinite Sets
Posted: May 12, 2011 11:18 AM
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On May 11, 8:21 pm, "Jesse F. Hughes" <> wrote:
> Tim Little <> writes:
> > As noted in a different branch, this should have been aleph_1 instead
> > of aleph_0 throughout.

> I assume (though I could be mistaken) that Katz's notion of set size
> also satisfies trichotomy.

"First, there is the principle of trichotomy.
(TRICH) x < y v x ~ y v x > y
which says that any two sets are comparable in size. While a theory of
set size
which excluded TRICH might escape ridicule, it would surely be
regarded with
suspicion. Indeed, if the principles of common sense were incompatible
TRICH, this would undoubtedly be used to discredit them."
(Katz, page 12)

> He does show it's a linear order, right, TP?

"(ASYM<) x < y -> not(y < x)
(TRANS<) (x < y & y < z) -> x < z
(IRREF<) not(x < x)"
(Katz, pages 11-13)

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