The combinatorics of the Baer-Specker group

We study subgroups of ℤ^ℕ which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Kočinac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Kočinac, and Scheepers. The first author was supported by the EU Research and Training Network HPRN-CT-2002-00287. The second author was partially supported by the Koshland Center for Basic Research.