Trivial automorphisms

Ilijas Farah*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageEnglish
Pages (from-to)701-728
Number of pages28
JournalIsrael Journal of Mathematics
Volume201
Issue number2
DOIs
StatePublished - 2 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, Hebrew University Magnes Press.

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