Forcing a Boolean algebra with predesigned automorphism group
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- by Tapani Hyttinen and Saharon Shelah PDF
- Proc. Amer. Math. Soc. 130 (2002), 2837-2843 Request permission
Abstract:
For suitable groups $G$ we will show that one can add a Boolean algebra $B$ by forcing in such a way that $Aut(B)$ is almost isomorphic to $G$. In particular, we will give a positive answer to the following question due to J. Roitman: Is $\aleph _{\omega }$ a possible number of automorphisms of a rich Boolean algebra?References
- Judy Roitman, The number of automorphisms of an atomic Boolean algebra, Pacific J. Math. 94 (1981), no. 1, 231–242. MR 625822, DOI 10.2140/pjm.1981.94.231
- J. D. Monk, Automorphism groups, J. D. Monk and R. Bonnet (ed.) Handbook of Boolean Algebras, vol. 2, North-Holland, Amsterdam, 1989, 517-546.
Additional Information
- Tapani Hyttinen
- Affiliation: Department of Mathematics, P.O. Box 4, 00014 University of Helsinki, Finland
- Email: thyttine@helsinki.fi
- Saharon Shelah
- Affiliation: Institute of Mathematics, The Hebrew University, Jerusalem, Israel – and – Rutgers University, Department of Mathematics, New Brunswick, New Jersey
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
- Received by editor(s): January 31, 2001
- Received by editor(s) in revised form: May 14, 2001
- Published electronically: March 14, 2002
- Additional Notes: The first author was partially supported by the Academy of Finland, grant 40734, and the Mittag-Leffler Institute
The research of the second author was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. Publ. 756 - Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2837-2843
- MSC (2000): Primary 06E05; Secondary 03E35
- DOI: https://doi.org/10.1090/S0002-9939-02-06399-2
- MathSciNet review: 1908905