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Ramsey Classes and Homogeneous Structures

Published online by Cambridge University Press:  15 February 2005

JAROSLAV NEšETŘIL
JAROSLAV NEšETŘIL
Affiliation:
Department of Applied Mathematics and Institute of Theoretical Computer Sciences (ITI), Charles University, Malostranské nám. 25, 11800 Praha, Czech Republic (e-mail: nesetril@kam.ms.mff.cuni.cz)
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Abstract

We present a programme of characterizing Ramsey classes of structures by a combination of the model theory and combinatorics. In particular, we relate the classification programme of countable homogeneous structures (of Lachlan and Cherlin) to the classification of Ramsey classes. As particular instances of this approach we characterize all Ramsey classes of graphs, tournaments and partial ordered sets. We fully characterize all monotone Ramsey classes of relational systems (of any type). We also carefully discuss the role of (admissible) orderings which lead to a new classification of Ramsey properties by means of classes of order-invariant objects.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 14 , Issue 1-2 , January 2005 , pp. 171 - 189
Copyright
© 2005 Cambridge University Press

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