In this paper we will define a cardinal invariant corresponding to the independence number for partitions of ω. By using Cohen forcing we will prove that this cardinal invariant is consistently smaller than the continuum.

The edge clique cover number ecc ( G ) of a graph is the size smallest collection complete subgraphs whose union covers all edges G. Chen, Jacobson, Kézdy, Lehel, Scheinerman, and Wang conjectured in 2000 that if claw-free, then bounded above by its order (denoted n). Recently, Javadi Hajebi verified this conjecture for claw-free graphs with an independence at least three. We study two, which a...