Embeddings into ${\cal P}({\Bbb N})/{\rm fin}$ and extension of automorphisms

Tom 174 / 2002

A. Bella, A. Dow, K. P. Hart, M. Hrusak, J. van Mill, P. Ursino Fundamenta Mathematicae 174 (2002), 271-284 MSC: Primary 06E99; Secondary 03E35, 03E50, 54G05. DOI: 10.4064/fm174-3-7

Streszczenie

Given a Boolean algebra ${\mathbb B}$ and an embedding $e:{\mathbb B}\to {\cal P} ({\mathbb N})/{\rm fin}$ we consider the possibility of extending each or some automorphism of ${\mathbb B}$ to the whole $ {\cal P}({\mathbb N})/{\rm fin}$. Among other things, we show, assuming ${\rm CH}$, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

Autorzy

  • A. BellaDipartimento di Matematica
    Università di Catania
    95125 Catania, Italy
    e-mail
  • A. DowMathematics Department
    UNC Charlotte
    9201 University City Blvd.
    Charlotte, NC 28223, U.S.A.
    e-mail
  • K. P. HartFaculty of Information Technology and Systems
    TU Delft
    Postbus 5031
    2600 GA Delft, The Netherlands
    e-mail
  • M. HrusakDivision of Mathematics
    Faculty of Sciences
    Vrije Universiteit
    De Boelelaan 1081a
    1081 HV Amsterdam, The Netherlands
    e-mail
  • J. van MillDivision of Mathematics
    Faculty of Sciences
    Vrije Universiteit
    De Boelelaan 1081a
    1081 HV Amsterdam, The Netherlands
    e-mail
  • P. UrsinoDipartimento di Matematica
    Università di Catania
    95125 Catania
    Italy
    e-mail

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