Authors: Farah, Ilijas 
Shelah, Saharon
Title: Trivial automorphisms
Journal: Israel Journal of Mathematics
Volume: 201
Issue: 2
First page: 701
Last page: 728
Issue Date: 1-Jan-2014
Rank: M21
ISSN: 0021-2172
DOI: 10.1007/s11856-014-1048-5
Abstract: 
We prove that the statement ‘For all Borel ideals I and J on ω, every isomorphism between Boolean algebras P(ω)/I and P(ω)/J has a continuous representation’ is relatively consistent with ZFC. In this model every isomorphism between P(ω)/I and any other quotient P(ω)/J over a Borel ideal is trivial for a number of Borel ideals I on ω.We can also assure that the dominating number, σ, is equal to ℵ1 and that (Formula presented.). Therefore, the Calkin algebra has outer automorphisms while all automorphisms of P(ω)/Fin are trivial.Proofs rely on delicate analysis of names for reals in a countable support iteration of Suslin proper forcings.
Publisher: Springer Link
Project: United States–Israel Binational Science Foundation, Grant no. 2010405
National Science Foundation, Grant no. DMS 1101597

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