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)^n_(i=1),≤,(≾_i)^n_(i=1), where ≤ is a total ordering on A and ≾_i is a linear ordering on the set {ɑ, є A : I_i(ɑ)}. The second class contains structures of the form (ɑ,≤,(i_i)^n_i=1,≾), where (A,≤) is a weak ordering and ≤ is a linear ordering on A such that A is partitioned by {ɑ, є A : I_i(ɑ)} into maximal chains in the partial ordering ≤ and each {ɑ, є A : I_i(ɑ)} is an interval with respect to.