Martin’s Axiom is consistent with the existence of nowhere trivial automorphisms
Authors:
Saharon Shelah and Juris Steprāns
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
Full-text PDF Free Access
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.
- Tomek Bartoszyński and Haim Judah, Set theory, A K Peters, Ltd., Wellesley, MA, 1995. On the structure of the real line. MR 1350295
- Saharon Shelah and J. Steprāns, Nontrivial homeomorphisms of $\beta {\bf N}_s {\bf N}$ without the continuum hypothesis, Fund. Math. 132 (1989), no. 2, 135–141. MR 1002627, DOI https://doi.org/10.4064/fm-132-2-135-141
- Saharon Shelah and Juris Steprāns, Somewhere trivial autohomeomorphisms, J. London Math. Soc. (2) 49 (1994), no. 3, 569–580. MR 1271551, DOI https://doi.org/10.1112/jlms/49.3.569
- Boban Veličković, Definable automorphisms of ${\scr P}(\omega )/{\rm fin}$, Proc. Amer. Math. Soc. 96 (1986), no. 1, 130–135. MR 813825, DOI https://doi.org/10.1090/S0002-9939-1986-0813825-8
- Boban Veličković, ${\rm OCA}$ and automorphisms of ${\scr P}(\omega )/{\rm fin}$, Topology Appl. 49 (1993), no. 1, 1–13. MR 1202874, DOI https://doi.org/10.1016/0166-8641%2893%2990127-Y
Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03E50, 03E35
Retrieve articles in all journals with MSC (1991): 03E50, 03E35
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
MR Author ID:
160185
ORCID:
0000-0003-0462-3152
Email:
shelah@math.rutgers.edu
Juris Steprāns
Affiliation:
Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3
Email:
steprans@yorku.ca
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