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# Indicators, Chains, Antichains, Ramsey Property

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Published:2013-09-10
Printed: Sep 2014
• 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
 MSC Classifications: 05C55 - Generalized Ramsey theory [See also 05D10] 03C15 - Denumerable structures 54H20 - Topological dynamics [See also 28Dxx, 37Bxx]

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