[FOM] Foreman's preface to HST
Monroe Eskew
meskew at math.uci.edu
Tue Apr 27 00:45:03 EDT 2010
On Sat, Apr 24, 2010 at 6:30 PM, <joeshipman at aol.com> wrote:
>
> Secondly, most of the natural independence-from-ZFC statements in the
> non-Absolute part of mathematics, such as the Continuum Hypothesis,
> have no additional consistency strength and can be shown independent by
> forcing arguments that can be formulated syntactically or in a much
> smaller set-theoretic universe that does not essentially depend on "the
> higher infinite".
I'm not sure what you mean by "natural," but there are many statements
about everyday sets that have pretty high consistency strength. A few
examples:
1) The Axiom of Determinacy.
2) SCH fails at \aleph_{\omega}.
3) All projective sets are Lebesgue measurable.
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