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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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?
- Judy Roitman, The number of automorphisms of an atomic Boolean algebra, Pacific J. Math. 94 (1981), no. 1, 231–242. MR 625822
- J. D. Monk, Automorphism groups, J. D. Monk and R. Bonnet (ed.) Handbook of Boolean Algebras, vol. 2, North-Holland, Amsterdam, 1989, 517-546.
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 06E05, 03E35
Retrieve articles in all journals with MSC (2000): 06E05, 03E35
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.
Article copyright:
© Copyright 2002
American Mathematical Society
