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Re: Order-preserving embeddings of ordinals in the real numbers
Posted:
Jul 28, 2006 12:00 PM
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Any finite linear ordering can be embedded in Q. Any countable model
of Th(Q) is isomorphic to Q. Hence any countable linear ordering can
be embedded into Q, by compactness and lowenheim skolem using the
above, and the diagram of the l.o. in question.
So all countable well orderings (i.e. < omega_1). Of the top of
my head (on my first coffee of the day), I'd say you'd have
problems with point whose cofinality was greater than omega,
since R is forst countable.
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