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 language | English |
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Pages (from-to) | 701-728 |
Number of pages | 28 |
Journal | Israel Journal of Mathematics |
Volume | 201 |
Issue number | 2 |
DOIs | |
State | Published - 2 Oct 2014 |
Bibliographical note
Publisher Copyright:© 2014, Hebrew University Magnes Press.