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ISSN 1088-6826(e) ISSN 0002-9939(p)

Martin's Axiom is consistent with the existence of nowhere trivial automorphisms

Author(s): Saharon Shelah; Juris Steprans
Journal: Proc. Amer. Math. Soc. 130 (2002), 2097-2106.
MSC (1991): Primary 03E50, 03E35
Posted: December 27, 2001
MathSciNet review: 1896046
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Abstract | References | Similar articles | Additional information

Abstract: Martin's Axiom does not imply that all automorphisms of ${\mathcal P}(\mathbb{N} )/ [\mathbb{N} ]^{<\aleph_0}$ are somewhere trivial. An alternate method for obtaining models where every automorphism of ${\mathcal P}(\mathbb{N} )/[\mathbb{N} ]^{<\aleph_0}$ is somewhere trivial is explained.

References:

1.: Tomek Bartoszynski and Haim Judah. Set Theory -- On the structure of the real line. A K Peters, 1995. MR 96k:03002
2.: S. Shelah and J. Steprans. Non-trivial homeomorphisms of $\beta {N}\setminus {N}$ without the Continuum Hypothesis. Fund. Math., 132:135-141, 1989. MR 90h:54015
3.: S. Shelah and J. Steprans. Somewhere trivial autohomeomorphisms. J. London Math. Soc. (2), 49:569-580, 1994. MR 95f:54008
4.: B. Velickovic. Definable automorphisms of ${\mathcal P}(\omega)/fin$ . Proc. Amer. Math. Soc., 96:130-135, 1986. MR 87m:03070
5.: Boban Velickovic. and automorphisms of ${\mathcal P}(\omega)/{\textit{fin}}$ . Topology Appl., 49(1):1-13, 1993. MR 94a:03080

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Additional Information:

Saharon Shelah
Affiliation: Department of Mathematics, Rutgers University, Hill Center, Piscataway, New Jersey
Address at time of publication: Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
Email: shelah@math.rutgers.edu

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

DOI: 10.1090/S0002-9939-01-06280-3
PII: S 0002-9939(01)06280-3
Keywords: Boolean algebra, Martin's Axiom, automorphism
Received by editor(s): October 12, 2000
Received by editor(s) in revised form: January 12, 2001
Posted: December 27, 2001
Additional Notes: The research of the first author was supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities, and by NSF grant No. NSF-DMS97-04477. Research of the second author for this paper was partially supported by NSERC of Canada. This is paper number 735 in the first author's personal listing
Communicated by: Alan Dow
Copyright of article: Copyright 2001, American Mathematical Society

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