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Forcing a Boolean algebra with predesigned automorphism group

Author(s): Tapani Hyttinen; Saharon Shelah
Journal: Proc. Amer. Math. Soc. 130 (2002), 2837-2843.
MSC (2000): Primary 06E05; Secondary 03E35
Posted: March 14, 2002
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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:

[Ro]
J. Roitman, The number of automorphism of an atomic Boolean algebra, Pacific Journal of Mathematics, vol. 94 (1981), 231-242. MR 82j:03064

[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: 10.1090/S0002-9939-02-06399-2
PII: S 0002-9939(02)06399-2
Received by editor(s): January 31, 2001
Received by editor(s) in revised form: May 14, 2001
Posted: 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 of article: Copyright 2002, American Mathematical Society

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