The University of California, Irvine

**Abstract:**

The set theorist Hugh Woodin has essentially proved that
every theory that fails to prove not-CH must suffer from certain other
mathematical defects. If defective theories should be
rejected, and sinceWoodin has produced at least one non-defective
theory, it follows that the continuum hypothesis should be
rejected. This
argument differs significantly from past attempts to settle CH because
it does not require one to adopt a specific theory. Rather, any
theory in the set of non-defective ones will do. We will argue
that if the characterization of defectiveness is modified in what
appears to be a
benign way, then ther are theories that imply CH without being
defective. We hope to make it seem plausible, then, that future
attempts to settle
CH will be like past ones: specific theories that settle CH will
have to be compared and one selected.

SST 777

3 pm

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