Abstract
We prove that it is relatively consistent with the usual ax- ioms of mathematics that all automorphisms of the Calkin algebra are inner. Together with a 2006 Phillips{Weaver construction of an outer automorphism using the Continuum Hypothesis, this gives a complete solution to a 1977 problem of Brown{Douglas{Fillmore. We also give a simpler and self-contained proof of the Phillips{Weaver result.
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