Summary
We prove that the automorphism group ofP(ω)/fin remains simple if ℵ2 Cohen reals are added to a model of ZFC+CH.
Similar content being viewed by others
References
Anderson, R.D.: The algebraic simplicity of certain groups of homeomorphisms. Am. J. Math.80, 955–963 (1958)
Van Douwen, E.: The automorphismus group ofP(N)/fin need not be simple. Preprint
Van Douwen, E., Monk, J.D., Rubin, M.: Some questions about Boolean algebras. Algebra Univers.11, 220–243 (1980)
Fuchino, S.: On the automorphism group ofP(N)/fin. Berlin: Dissertation 1988
Jech, Th.: Set theory. New York, San Francisco, London: Academic Press 1978
Koppelberg, S.: Homogeneous Boolean algebras may have non-simple automorphism groups. Top. Appl.21, 103–120 (1985)
Koppelberg, S.: General Theory of Boolean Algebras. In: Monk, D.J., Bonnet, R.: Handbook of Boolean algebras, vol. 1, pp. 1–312. Amsterdam New York Oxford Tokyo: North-Holland 1989
Kunen, K.: Set theory. Amsterdam New York Oxford: North-Holland 1980
Van Mill, J.: An introduction to βω. In: Kunen, K., Vaughan, J.E. (eds.). Handbook of set-theoretic topology, pp. 503–568. Amsterdam New York Oxford: North-Holland 1985
Štěpánek, P., Rubin, M.: Homogeneous Boolean algebras. In: Monk, J., Bonnet, R. (eds.). Handbook of Boolean algebras, vol. 2, pp. 679–687. Amsterdam New York Oxford Tokyo: North-Holland 1989
Shelah, S.: Proper Forcing. Lect. Notes Math.940, 1–496 (1982)
Shelah, S., Steprāns, J.: Non-trivial automorphisms of βN/N without the continuum hypothesis. Fund. Math.132, 135–141 (1989)
Shelah, S., Steprāns, J.: PFA implies all automorphisms are trivial. Proc. Amer. Math. Soc.104, 1220–1225 (1988)
Veličković, B.: Definable automorphisms of 330-5k. Proc. Amer. Math. Soc.96, 130–135 (1986)
Veličković, B.: OCA and automorphisms ofP(ω)/fin. Top. Appl. (to appear)
Author information
Authors and Affiliations
Additional information
This paper is based on a part of author's Dissertation [4] written under the supervision of Professor Sabine Koppelberg whom the author would like to thank for her encouragement during the preparation of the thesis. Thanks are also due to the referee for some valuable suggestions on improvement of the formulation
Rights and permissions
About this article
Cite this article
Fuchino, S. On the simplicity of the automorphism group ofP(ω)/fin. Arch Math Logic 31, 319–330 (1992). https://doi.org/10.1007/BF01627505
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01627505