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SET IDEALS WITH ISOMORPHIC SYMMETRY GROUPS

Published online by Cambridge University Press:  18 January 2002

PETER BIRYUKOV  and
VALERY MISHKIN
PETER BIRYUKOV
Affiliation:
Department of Mathematics, Kemerovo State University, Kemerovo 650043, Russia; stbpa@ic.kemsu.ru
VALERY MISHKIN
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada; vmishkin@mathstat.yorku.ca
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Abstract

A criterion of isomorphism for symmetry groups of set ideals is provided in terms of ideal quotients and cardinal invariants. Furthermore, set ideals with complete symmetry group are characterized. They form a wide class, comprising, for example, all uniform dense ideals and the ideals of ‘thin’ sets in separable metric spaces. If the symmetry group of a set ideal is not complete, then its outer automorphism group is shown to be cyclic of order 2.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 1 , January 2002 , pp. 37 - 45
Copyright
© The London Mathematical Society 2002

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