[FOM] The Continuum Hypothesis

Joan Bagaria joan.bagaria at aaupc.upcnet.es
Sun May 18 17:39:59 EDT 2003

Reply to Sephorah Mangin:

>2) Is there any general consensus amongst the mathematical/FOM community
regarding the truth or falsity of CH?

I believe that some recent results on the continuum problem, most of them by
Woodin, may lead in the next few years to a more or less general consensus
among set theorists that the most reasonable cardinality for the continuum
is aleph_2.

>3) What are the most important recent developments post-Cohen which have
contributed to this consensus (or lack thereof)?

The most important contributions are due to Woodin. Besides the two survey
papers by Woodin referenced in Mathias' yesterday posting, I would like to
recommend Patrick Dehornoy's survey paper on Woodin's work on the Continuum
Hypothesis, recently presented at the Seminaire Bourbaki. It is available,
both in French and English, at Patrick's home page

>Have set-theorists proposed any plausible axioms which might decide CH?

Yes. One example is Woodin's (*) axiom. Another is the Bounded Martin's
Maximum (BMM). Both imply that the size of the continuum is aleph_2.

Joan Bagaria
Institució Catalana de Recerca i Estudis Avançats (ICREA) and
Departament de Lògica, Història i Filosofia de la Ciència
Universitat de Barcelona
e-mail: bagaria at trivium.gh.ub.es

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