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


Authors: Saharon Shelah and Juris Steprans
Journal: Proc. Amer. Math. Soc. 130 (2002), 2097-2106
MSC (1991): Primary 03E50, 03E35
DOI: https://doi.org/10.1090/S0002-9939-01-06280-3
Published electronically: December 27, 2001
MathSciNet review: 1896046
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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.

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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: https://doi.org/10.1090/S0002-9939-01-06280-3
Keywords: Boolean algebra, Martin's Axiom, automorphism
Received by editor(s): October 12, 2000
Received by editor(s) in revised form: January 12, 2001
Published electronically: 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
Article copyright: © Copyright 2001 American Mathematical Society