×

A pigeonhole property for relational structures. (English) Zbl 0932.03033

Summary: We study those relational structures \(S\) with the property \(({\mathcal P})\) that each partition of \(S\) contains a block isomorphic to \(S\). We show that the Fraïssé limits of parametric classes \({\mathcal K}\) have property \(({\mathcal P})\); over a binary language, every countable structure in \({\mathcal K}\) satisfying \(({\mathcal P})\) along with a condition on 1-extensions must be isomorphic to this limit.

MSC:

03C15 Model theory of denumerable and separable structures
03C50 Models with special properties (saturated, rigid, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cameron, London Math. Soc. Lecture Notes 152, in: Oligomorphic Permutation Groups (1990)
[2] Cameron, The random graph, Algorithms and Combinatorics 14 pp 333– (1997) · Zbl 0864.05076
[3] Ebbinghaus, Finite Model Theory (1995) · Zbl 0841.03014
[4] Henson, A family of countable homogeneous graphs, Pacific J. Math. 38 pp 69– (1971) · Zbl 0204.24103
[5] Hodges, Encyclopedia of Mathematics and its Applications 42, in: Model Theory (1994)
[6] Oberschelp, Lecture Notes in Mathematics 969, in: Asymptotic 0-1 laws in combinatorics pp 276– (1982) · Zbl 0515.05001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.