I shall first review previous joint work with Arthur Apter and with Moti Gitik in which choiceless forms of the singular cardinal hypothesis are strongly violated in symmetric models. In the PhD project of my student Anne Fernengel we have obtained similar results for all regular and singular cardinals, in analogy with Easton's famous theorem. Define the θ-function

θ(κ) = sup { α : ∃ f : P( κ ) ↠ α }

In a ground model of ZFC + GCH let F be a function from cardinals to cardinals, which is weakly monotonous and satisfies

∀ κ F( κ) ≥ κ⁺⁺

Then there is a cardinal preserving symmetric extension in which

∀ κ θ(κ)=F(κ).