[Date Index] [Thread Index] [FOM Postings] [FOM Home]

*To*: fom@math.psu.edu*Subject*: FOM: De Branges claims to have shown measurable cardinals inconsistent*From*: Joe Shipman <shipman@savera.com>*Date*: Mon, 19 Jul 1999 11:55:46 -0400*Organization*: Savera systems*Sender*: owner-fom@math.psu.edu

Louis De Branges of Purdue University has claimed on his web page http://www.math.purdue.edu/~branges/ to have shown that no nontrivial countably additive measure exists on all subsets of the continuum (which by Solovay implies that there are no measurable cardinals). His manuscript is available at ftp://ftp.math.purdue.edu/pub/branges/ , along with manuscripts containing purported proofs of the invariant subspace conjecture and the Riemann Zeta Hypothesis and an autobiographical "apology" which explains the mathematical motivation for his Riemann Hypothesis proof and reveals that he proved the Bieberbach conjecture so that he could get funding to work on the Riemann Hypothesis. The "Measure Problem" manuscript begins with a generalization of Stone's proof of the Hahn-Banach theorem to apply to "hyperconvex sets". The last 5 pages apply this representation theorem to obtain the result on measures. De Branges uses nonstandard terminology for the set-theoretical part of the paper, which makes it more difficult to follow. It would be easy to dismiss De Branges as a crank because of this, but he has earned the right to a hearing because the early dismissals of his work on the Bieberbach Conjecture turned out to be wrong. As far as I can tell, his Riemann Hypothesis and Invariant Subspace manuscripts are more conventional in their terminology. Although a refutation of measurable cardinals would be very surprising, and I strongly doubt De Branges has accomplished this, other eminent mathematicians who are experts in the field have admitted to trying to refute measurable cardinals, and the example of Cohen shows that it is not necessary to be a specialist in set theory to make a breakthrough in the field. -- Joe Shipman

[Date Prev] [Date Next] [Thread Prev] [Thread Next]

[Date Index] [Thread Index] [FOM Postings] [FOM Home]