[FOM] Davis's honor Roll

William Tait wwtx at earthlink.net
Tue Jun 3 23:26:05 EDT 2003

On Tuesday, June 3, 2003, at 04:05  AM, praatika at mappi.helsinki.fi 

> Another potential example: it seems to me that in the beginning (ca 
> 1938)
> Godel believed in the truth of V=L (not only in its consistency). Quite
> probably he also believed in the existence of the large cardinals, in
> particular in the existence of measurable cardinals. This, however, is
> consistent. Any comments on that?

In ``What is Cantor's continuum problem?'', Goedel has a footnote 
(added to the version in the Benacerraf/Putnam volume (1964)) in which 
he states that the existence of measurable cardinals (unlike that of, 
e.g., Mahlo cardinals) does not follow from the conception of set that 
he there develops. He also refers there to Scott's proof that V=L is 
inconsistent with the existence of measurable cardinals. In one of his 
introductory essays to Goedel's papers on set theory, Solovay remarks 
that Goedel believed in the existence of measurable cardinals---I don't 
offhand remember the details; but I expect that such a belief would 
certainly have been formed later, when Goedel was fully aware that it 
was inconsistent with V=L.

Bill Tait

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