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In 1980, Erdős, Rubin and Taylor asked whether for all positive integers a, b, and m, every (a : b)-choosable graph is also (am : bm)-choosable. We provide a negative answer by exhibiting a 4-choosable graph that is not (8 : 2)-choosable.Coloring the vertices of a graph with sets of colors (that is, each vertex is assigned a fixed-size subset of the colors such that adjacent vertices are assigned disjoint sets) is a fundamental notion, which in particular captures fractional colorings. The fractional chromatic number of a graph G can indeed be defined to be the infimum (which actually is a minimum) of the ratios a/b such that, if every vertex of G is replaced by a clique of order b and every edge of G is replaced by a complete bipartite graph between the relevant cliques, then the chromatic number of the obtained graph is at most a.In their seminal work on list coloring, Erdős, Rubin and Taylor [2] raised several intriguing questions about the list version of set coloring. Before stating them, let us review the relevant definitions. Set coloring.A function that assigns a set to each vertex of a graph is a set coloring if the sets assigned to adjacent vertices are disjoint. For positive integers a and b ≤ a, an (a : b)-coloring of a graph G is a set coloring with range {1,...,a} b , i.e., a set coloring that to each vertex of G assigns a b-element subset of {1, . . . , a}. The concept of (a : b)-coloring is a generalization of the conventional vertex coloring. In fact, an (a : 1)-coloring is exactly an ordinary proper a-coloring.A list assignment for a graph G is a function L that to each vertex v of G assigns a set L(v) of colors. A set coloring ϕ of G is an L-set coloring if ϕ(v) ⊆ L(v) for every v ∈ V (G). For a positive integer b, we say that ϕ is anFor an integer a ≥ b, we say that G is (a : b)-choosable if G is (L : b)-colorable for every list assignment L * This project falls within the scope of L.I.A. STRUCO.