On May 11, 8:21 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > Tim Little <t...@little-possums.net> 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 with 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)