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We show that the abstract commensurator of Thompson's group F is composed offour building blocks: two isomorphism types of simple groups, themultiplicative group of the positive rationals and a cyclic group of order two.The main result establishes the simplicity of a certain group of piecewiselinear homeomorphisms of the real line.

Addendum to "Commensurations and Subgroups of Finite Index of Thompson's Group F"