# All automorphisms of all Calkin algebras - Mathematics > Logic

Abstract: The Proper Forcing Axiom implies all automorphisms of every Calkin algebraassociated with an infinite-dimensional complex Hilbert space and the ideal ofcompact operators are inner. As a means of the proof we introduce the notion ofPolish $\omega 1$-trees and cohrerent families of Polish spaces and prove someuniformization results.

Author: Ilijas Farah

Source: https://arxiv.org/