Decisive creatures and large continuum

For f, g ∈ ω^ω let c_f,g ^∀ be the minimal number of uniform g-splitting trees (or: Slaloms) to cover the uniform f-splitting tree, i.e., for every branch v of the f-tree, one of the g-trees contains v. c_f,g^∃ is the dual notion: For every branch v, one of the g-trees guesses v(m) infinitely often. It is consistent that c_fε,gε^∃ = c_fε,gε^∀ = k_ε for N ₁ manypairwise different cardinals k_ε and suitable pairs (fε,gε). For the proof we use creatures with sufficient bigness and halving. We show that the lim-inf creature forcing satisfies fusion and pure decision. We introduce decisiveness and use it to construct a variant of the countable support iteration of such forcings, which still satisfies fusion and pure decision.