[FOM] Order types: a proof

Moses Klein klein at math.ohiou.edu
Mon Mar 7 01:31:30 EST 2005

JoeShipman at aol.com said:
> Can anyone provide an EXPLICIT (choiceless) construction of
> an example not isomorphic to one of the 11 obtained from
> the "real" examples above by replacing the reals with the
> rationals in the obvious way?  It's nice to show that there
> are 2^aleph-1 of them with a stationary set argument, but it
> ought to be possible to get just one more without going
> through such advanced combinatorics.

Stick with Dave Marker's solution -- you can't explicitly get
2^aleph-1 distinct-mod-NS sets, but you can get two. If S=omega_1 then
A^S is Q x omega-1; if S=emptyset then A^S is Q + (1+Q) x omega-1.
These are nonisomorphic, as omega-1 embeds continuously into the
latter but not the former.

Moses Klein
Visiting Assistant Professor
Department of Mathematics
Ohio University
Athens, OH  45701,  USA
klein at math.ohiou.edu

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