### Rigidity of continuous quotients

by Farah and Shelah. [FaSh:1042]

J Institute of Math at Jussieu, 2016

The assertion that the Cech--Stone remainder of the half-line
has only trivial automorphisms is independent from ZFC. The
consistency of this statement follows from Proper Forcing Axiom
and this is the first known example of a connected space with this
property. The existence of 2^{aleph_1} autohomeomorphisms under
the Continuum Hypothesis follows from a general model-theoretic fact.
We introduce continuous fields of metric models and prove countable
saturation of the corresponding reduced products. We also provide an
(overdue) proof that the reduced products of metric models
corresponding to the Frechet ideal are countably saturated. This
provides an explanation of why the asymptotic sequence C*- algebras
and the central sequence C*-algebras are as useful as ultrapowers.

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