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Journal of the London Mathematical Society 1995 52(2):303-317; doi:10.1112/jlms/52.2.303
© 1995 by London Mathematical Society
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© The London Mathematical Society

Homogeneous Families and their Automorphism Groups

Menachem Kojman and Saharon Shelah

Department of Mathematics, Carnegie Mellon University Pittsburgh, Pennsylvania 15213, USA E-mail: kojman{at}andrew.cmu.edu
Institute of Mathematics, Hebrew University of Jerusalem Givat Ram, 91904 Jerusalem, Israel Rutgers University New Brunswick, New Jersey, USA E-mail: shelah{at}math.huji.ac.il

Received 5 August 1993. Revision received 18 April 1994.

A homogeneous family of subsets over a given set is one with a very ‘rich’ automorphism group. We prove the existence of bi-universal element in the class of homogeneous families over a given infinite set and give an explicit construction of Formula isomorphism types of homogeneous families over a countable set.

Research of the first author was partially supported by the Edmund Landau Center for research in Mathematical Analysis, sponsored by the Minerva Foundation (Germany).

The second author thanks the Israeli Academy of Sciences for partial support. Publication number 499.


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