Canonical Vertex Partitions
Published online by Cambridge University Press: 03 December 2003
Abstract
Let σ be a finite relational signature, let be a set of finite complete relational structures of signature σ, and let be the countable homogeneous relational structure of signature σ which does not embed any of the structures in .
When σ consists of at most binary relations and is finite, the vertex partition behaviour of is completely analysed, in the sense that it is shown that a canonical partition exists and the size of this partition in terms of the structures in is determined. If is infinite some results are obtained, but a complete analysis is still missing.
Some general results are presented which are intended to be used in further investigations when σ contains relational symbols of arity larger than two or when the set of bounds is infinite.
- Type
- Research Article
- Information
- Combinatorics, Probability and Computing , Volume 12 , Issue 5-6: This issue contains volume twelve, parts five and six , November 2003 , pp. 671 - 704
- Copyright
- Copyright © Cambridge University Press 2003
Footnotes
Supported by NSERC of Canada grant # 691325
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