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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