Decisive creatures and large continuum

A. For f > g ∈ ω let c∀f ,g be the minimal number of uniform trees with g-splitting needed to ∀-cover the uniform tree with f -splitting. c∃f ,g is the dual notion for the ∃ cover. Assuming CH and given א1 many (sufficiently different) pairs ( f2 , g2 ) and cardinals κ2 such that κ0 2 = κ2 , we construct a partial order forcing that c∃f2 ,g2 = c ∀ f2 ,g2 = κ2 . For this, we introduce a countable support semiproduct of decisive creatures with bigness and halving. This semiproduct satisfies fusion, pure decision and continuous reading of names.