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Automorphisms of $\mathcal P(\lambda )/\mathcal I_\kappa $

Volume 233 / 2016

Paul Larson, Paul McKenney Fundamenta Mathematicae 233 (2016), 271-291 MSC: Primary 03E35; Secondary 06E05. DOI: 10.4064/fm129-12-2015 Published online: 2 December 2015

Abstract

We study conditions on automorphisms of Boolean algebras of the form $\mathcal P(\lambda )/\mathcal I_{\kappa }$ (where $\lambda $ is an uncountable cardinal and $\mathcal I_{\kappa }$ is the ideal of sets of cardinality less than $\kappa $) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every automorphism of $\mathcal P(2^{\kappa })/\mathcal I_{\kappa ^{+}}$ which is trivial on all sets of cardinality $\kappa ^{+}$ is trivial, and that MA$_{\aleph _{1}}$ implies both that every automorphism of $\mathcal {P}(\mathbb {R})/\tt{Fin} $ is trivial on a cocountable set and that every automorphism of $\mathcal P(\mathbb R)/\tt {Ctble}$ is trivial.

Authors

  • Paul LarsonDepartment of Mathematics
    Miami University
    Oxford, OH 45056, U.S.A.
    e-mail
  • Paul McKenneyDepartment of Mathematics
    Miami University
    Oxford, OH 45056, U.S.A.
    e-mail

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