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Non-trivially isomorphic corona algebras
- Speaker(s)
- Saeed Ghasemi
- Affiliation
- IMPAN
- Date
- June 8, 2016, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar
It is well-known that there are
Cech-Stone remainders (corona spaces) of locally compact spaces for
which the question of whether they are homeomorphic is independent from
ZFC (e.g., the Cech-Stone remainders of the ordinals \omega and \omega^2, with the order topology). Therefore by the Gelfand duality between compact Hausdorff spaces and commutative C*-algebras, there are commutative C*-algebras, for which the question of whether they are isomorphic is independent from ZFC.
I
will present a tool in model theory for metric structures which allows
us to find non-commutative C*-algebras -which are corona of product of
full matrices- and are isomorphic
under CH, but for non-trivial reasons. On the other hand it is
consistent with ZFC that these corona algebras are only isomorphic if
there is a trivial reason for it.
The
model theory tool used here is a generalization of the classical
Feferman-Vaught Theorem to the reduced products of metric structures.
