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Forcing a Boolean algebra with predesigned automorphism group


Authors: Tapani Hyttinen and Saharon Shelah
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
Published electronically: March 14, 2002
MathSciNet review: 1908905
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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 [Enhancements On Off] (What's this?)

  • [Ro] Judy Roitman, The number of automorphisms of an atomic Boolean algebra, Pacific J. Math. 94 (1981), no. 1, 231–242. MR 625822
  • [Mo] J. D. Monk, Automorphism groups, J. D. Monk and R. Bonnet (ed.) Handbook of Boolean Algebras, vol. 2, North-Holland, Amsterdam, 1989, 517-546. CMP 21:10

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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
Email: shelah@math.huji.ac.il

DOI: https://doi.org/10.1090/S0002-9939-02-06399-2
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.
Article copyright: © Copyright 2002 American Mathematical Society