[FOM] Uniqueness of hyperreals and the Continuum Hypothesis

Robert L Knighten RLK at knighten.org
Sun Aug 17 22:32:35 EDT 2008

When constructing "the" hyperreals as a non-principal ultrapower of the real
numbers it is frequently mentioned that, assuming the Continuum Hypothesis,
all such ordered fields are order isomorphic.  It is also occasionally
mentioned that the converse is true as well -- failure of CH means it is
possible to construct non-isomorphic hyperreal fields.  I have located a proof
of the first of these results, but not of the second.  So a question for the
experts on FOM: is it true, and if so where is a proof to be found.

-- Bob

Robert L. Knighten
RLK at knighten.org

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