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The autohomeomorphism group of the Cech-Stone compactification of the integers


Author: Juris Steprans
Journal: Trans. Amer. Math. Soc. 355 (2003), 4223-4240
MSC (2000): Primary 03E35
DOI: https://doi.org/10.1090/S0002-9947-03-03329-4
Published electronically: June 10, 2003
MathSciNet review: 1990584
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown to be consistent that there is a nontrivial autohomeomorphism of $\beta{\mathbb N} \setminus {\mathbb N}$, yet all such autohomeomorphisms are trivial on a dense $P$-ideal. Furthermore, the cardinality of the autohomeomorphism group of $\beta{\mathbb N} \setminus {\mathbb N}$ can be any regular cardinal between $2^{\aleph_0}$ and $2^{2^{\aleph_0}}$. The model used is one due to Velickovic in which, coincidentally, Martin's Axiom also holds.


References [Enhancements On Off] (What's this?)

  • 1. Uri Abraham, Matatyahu Rubin, and Saharon Shelah,
    On the consistency of some partition theorems for continuous colorings, and the structure of $\aleph\sb 1$-dense real order types,
    Ann. Pure Appl. Logic, 29(2):123-206, 1985. MR 87d:03132
  • 2. Winfried Just,
    A modification of Shelah's oracle-c.c. with applications,
    Trans. Amer. Math. Soc., 329(1):325-356, 1992. MR 92j:03047
  • 3. S. Shelah,
    Proper Forcing, Lecture Notes in Mathematics, vol. 940,
    Springer-Verlag, Berlin, 1982. MR 84h:03002
  • 4. S. Shelah and J. Steprans,
    PFA implies all automorphism are trivial,
    Proc. Amer. Math. Soc., 104:1220-1225, 1988. MR 89e:03080
  • 5. S. Shelah and J. Steprans,
    Somewhere trivial autohomeomorphisms,
    J. London Math. Soc. (2), 49:569-580, 1994. MR 95f:54008
  • 6. Saharon Shelah,
    Proper and improper forcing, Perspectives in Mathematical Logic,
    Springer-Verlag, Berlin, second edition, 1998. MR 98m:03002
  • 7. S. Todorcevic,
    Partition Problems in Topology, Contemporary Mathematics, vol. 84,
    American Mathematical Society, Providence, RI, 1989. MR 90d:04001
  • 8. Boban Velickovic,
    Definable automorphisms of ${\mathcal {P}}(\omega)/{{fin}}$,
    Proc. Amer. Math. Soc., 96(1):130-135, 1986. MR 87m:03070
  • 9. Boban Velickovic,
    OCA and automorphisms of ${\mathcal {P}}(\omega)/{{fin}}$,
    Topology Appl., 49(1):1-13, 1993. MR 94a:03080

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Additional Information

Juris Steprans
Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
Email: steprans@yorku.ca

DOI: https://doi.org/10.1090/S0002-9947-03-03329-4
Received by editor(s): January 8, 2001
Received by editor(s) in revised form: March 10, 2003
Published electronically: June 10, 2003
Additional Notes: Research for this paper was partially supported by NSERC of Canada.
Article copyright: © Copyright 2003 American Mathematical Society

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