In this paper we introduce a measure of the extent to which a given finite poset deviates from being a Ramsey object in the class of finite posets. We show how this measure depends on the symmetry properties of a poset. containing a copy of Q, an r-colouring of [R, P] can be found which assumes, on
Symmetry and the Ramsey Degrees of Finite Relational Structures
✍ Scribed by Willem L. Fouché
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 134 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
In this paper, we introduce a measure of the extent to which a finite combinatorial structure is a Ramsey object in the class of objects with a similar structure. We show for classes of finite relational structures, including graphs, binary posets, and bipartite graphs, how this measure depends on the symmetries of the structure.
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We show that for every computably enumerable (c.e.) degree a¿0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is {0; a}, thus answering a question of Goncharov and Khoussainov (Dokl. Math. 55 (1997) 55-57). We also show
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