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Search: MSC category 05C55 ( Generalized Ramsey theory [See also 05D10] )

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1. CMB 2013 (vol 57 pp. 631)

Sokić, Miodrag
Indicators, Chains, Antichains, Ramsey Property
We introduce two Ramsey classes of finite relational structures. The first class contains finite structures of the form $(A,(I_{i})_{i=1}^{n},\leq ,(\preceq _{i})_{i=1}^{n})$ where $\leq $ is a total ordering on $A$ and $% \preceq _{i}$ is a linear ordering on the set $\{a\in A:I_{i}(a)\}$. The second class contains structures of the form $(A,\leq ,(I_{i})_{i=1}^{n},\preceq )$ where $(A,\leq )$ is a weak ordering and $% \preceq $ is a linear ordering on $A$ such that $A$ is partitioned by $% \{a\in A:I_{i}(a)\}$ into maximal chains in the partial ordering $\leq $ and each $\{a\in A:I_{i}(a)\}$ is an interval with respect to $\preceq $.

Keywords:Ramsey property, linear orderings
Categories:05C55, 03C15, 54H20

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