[FOM] Continuum Hypothesis Harvey Friedman friedman at math.ohio-state.edu
Sun May 18 01:35:25 EDT 2003 1) Do you believe that the continuum hypothesis is true, or false? I personally do not think about the continuum hypothesis in these terms. I think about *what kind of results would shed light on the status of the continuum hypothesis?* Here "status" means truth, falsity, and more broadly, notions of meaningfulness and meaninglessness. I have not succeeded in doing anything important on this, although I do have some ideas in this direction that I would like to pursue. They are just ideas. > 2) Is there any general consensus amongst the mathematical/FOM community regarding the truth or falsity of CH? 3) What are the most important recent developments post-Cohen which have contributed to this consensus (or lack thereof)? The lack of consensus as to meaningfulness has been fed by the fact that i) on the one hand, CH demonstrably holds in L, and in the analog of L where large cardinals abound (inner models), and ii) every (countable) model of every reasonable large cardinal hypothesis has plenty of forcing extensions in which CH fails. For some but not all, this casts doubt on the meaningfulness of CH. Also, the lack of a compelling thematically striking general principle about the nature of sets after such a long time, for some but not all, casts doubt on the meaningfulness of CH. Feferman has been most vocal among famous logicians that "CH is not meaningful". > | |
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