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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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
  • 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