Distributive Lattices and Hurewicz families
Mathematica Moravica, Tome 10 (2006) no. 1.

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Hurewicz and Rothberger respectively introduced prototypes of the selection properties $S_{fin}(A, B)$ and $S_1(A, B)$. In the series of papers titled “Combinatorics of open covers” (see the bibliography) we learned that for various topologically significant families $A$ and $B$ these selection properties are intimately related to game theory and Ramsey theory. The similarity in techniques used there to explore these relationships suggests that there should be a general, unified way to obtain these results. In this paper we pursue one possibility by considering the selection principle $S_{fin}(A, B)$ for distributive lattices. The selection principle $S_1(A, B)$ for distributive lattices will be treated in [3]. We use two examples throughout to illustrate the generality of the methods developed here.
Mots-clés : game, selection principle, lattice, A-tree, Hurewicz A-tree, Hurewicz pairs, Ramsey family, partition relation, selectable pair 
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Marion Scheepers. Distributive Lattices and Hurewicz families. Mathematica Moravica, Tome 10 (2006) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2006_10_1_a9/