### Abstract:

Two different themes in structural Ramsey (or partition) theory are addressed. The first is the partitioning of trees viewed as representations of certain posets. It follows from Fouché [Foua] that an obvious lower bound can be attained for the height of a tree <i>T</i> such that it has a monochromatic subtree of a given structure for an arbitrary <i>r</i>-colouring of the chains of <i>T</i> (of a specified length). In the first chapter a simultaneous bound on the arity of such a tree <i>T</i> of minimum height is found. The second theme concerns words over a given (possibly empty) alphabet and certain subsets of such words, the so-called <i>m</i>-parameter sets, which are associated with <i>m</i>-parameter words. A number of variations on themes by Hales and Jewett, Voigt, Graham and Rothschild, Milliken, Taylor and Fouché are developed. In the second chapter a formalization is given of a technique that occurs frequently in Ramsey theory and which is extensively used throughout the remaining chapters. It also includes a generalization of Shelah's Cube Lemma [She88] which plays a crucial role in providing a primitive recursive proof of Van der Waerden's theorem [vdW27] on arithmetic progressions. The remainder of that chapter is devoted to variations of the Hales-Jewett theorem [HJ63] for ascending parameter words, in the spirit of the *-version of Voigt [Voi80] The generalization of the Hales-Jewett theorem to the partitioning of <i>k</i>-parameter words by Graham and Rothschild required an induction on the number of parameters. Milliken [Mil75] and, independently, Taylor [Tay76], introduced new methods which led to a version of the Graham-Rothschild theorem for ascending parameter words of infinite length over an alphabet with one symbol. Fouché [Foua, Foub] proved the finite version using a constructive argument. In chapter 3 the technique used by Shelah [She88] in his proof of the Hales-Jewett theorem is applied to the Milliken-Taylor-Fouché result in order to prove the theorem for alphabets with more than one symbol. Some variations on this theme are developed. In the last chapter the idea of a multi-alphabet parameter word (restricted in the sense that parameters are only allowed in one of the alphabets) is introduced and it is shown that two- and three-alphabet versions of the Hales-Jewett and Graham-Rothschild theorems can be proved. For these results it is essential that the parameter words are ascending. Firstly, consideration is given to partitions of the left and right factors of words. Then a version of the Hales-Jewett theorem is derived where the partitions of factors of words now retains the information on the position of the factor in the word. Eventually analogous results are derived for <i>k</i>-parameter words. Some emphasis is placed on the subrecursive complexity of the results (all of which are primitive recursive).