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A complete partition theory is presented for omega-located words (andomega-words), namely for located words over an infinite alphabet dominated by afixed increasing sequence. This theory strengthens in an essential way theclassical Carlson, Furstenberg-Katznelson, and Bergelson-Blass-Hindmanpartition theory for words over a finite alphabet. Consequences of this theoryare strong simultaneous extensions of the classical Hindman, Milliken-Taylorpartition theorem, and of a van der Waerden theorem for general semigroups,extending results of Hindman-Strauss and Beiglbock.

Ramsey Theory for Words over an Infinite Alphabet