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Karagiannis: a combinatorial infinite Hales–Jewett proof
Nikolaos Karagiannis, "A combinatorial proof of an infinite version of the Hales--Jewett theorem," Journal of Combinatorics 4 (2013), no. 2, 273--291.
Karagiannis gives a combinatorial proof, resting on the classical Hales–Jewett theorem, of the infinite extension due to Carlson and, independently, Furstenberg and Katznelson (Theorem 2, p. 274), and of its version for an increasing sequence of finite alphabets (Theorem 3).
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