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The number of infinite substructures

Published online by Cambridge University Press:  24 October 2008

Dugald Macpherson ,
Alan H. Mekler  and
Saharon Shelah
Dugald Macpherson
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London El 4NS
Alan H. Mekler
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel
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Abstract

Given a relational structure M and a cardinal λ < |M|, let øλ denote the number of isomorphism types of substructures of M of size λ. It is shown that if μ < λ are cardinals, and |M| is sufficiently larger than λ, then øμ ≤ øλ. A description is also given for structures with few substructures of given infinite cardinality.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 1 , January 1991 , pp. 193 - 209
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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