|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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