[FOM] Alternative foundations?
jkennedy at mappi.helsinki.fi
jkennedy at mappi.helsinki.fi
Fri Feb 21 03:09:58 EST 2014
Set theory and category theory are bi-intepretable. As to the below:
> Category theory itself furnishes several examples of objects that
> have no existence in set theory, such as the category of all sets.
The category of all sets is interpreted in set theory as V_kappa,
kappa inaccessible.
> However, the main point of HTT as opposed to set theory, as I
> understand it, is not that set theory does not postulate enough
> sets, but that HTT allows one to formalize many parts of mathematics
> in a much less arbitrary manner than in set theory. Frenkel's remark
> that "mathematical structures constitute but a small island of
> modern mathematics" should perhaps be taken not to say that these
> parts would necessarily be unformalizable in set theory, but rather
> that such a formalization may not be the most useful or enlightening
> one.
>
> Staffan Angere
> University of Lund
>
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
--
Helsinki Collegium for Advanced Studies
Fabianinkatu 24 (P.O. Box 4)
00014 University of Helsinki
and
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FI-00014 University of Helsinki, Finland
tel. (+358-9)-191-51446, fax (+358-9)-191-51400
http://www.math.helsinki.fi/logic/people/juliette.kennedy/
More information about the FOM
mailing list