Logic & Philosophy of Science Colloquium


John Rapalino
  The University of California, Irvine

"The Status of the Continuum Hypothesis (CH) Today"


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.

Friday, June 8, 2007
SST 777
3 pm

Refreshments will be served