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Indicators, chains, antichains, Ramsey property

  • Miodrag Sokić,
    Mathematics Department, California Institute of Technology, Pasadena, California 91125
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Abstract

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 Ramsey property, linear orderings
MSC Classifications: 05C55, 03C15, 54H20 show english descriptions Generalized Ramsey theory [See also 05D10]
Denumerable structures
Topological dynamics [See also 28Dxx, 37Bxx]
05C55 - Generalized Ramsey theory [See also 05D10]
03C15 - Denumerable structures
54H20 - Topological dynamics [See also 28Dxx, 37Bxx]
 

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