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We show that in the theory ZF + DC + for every cardinal {\lambda}, the set ofinfinite subsets of {\lambda} is well-ordered (i.e., Shelah's AX4), the{\theta}-function measuring the surjective size of the powersets P({\kappa})can take almost arbitrary values on any set of uncountable cardinals. Thiscomplements our results from [FK16], where we prove that in ZF (without DC),any possible behavior of the {\theta}-function can be realized; and answers aquestion of Shelah in [She16], where he emphasizes that ZF + DC + AX4 is areasonable theory, where much of set theory and combinatorics is possible.

An Easton-like Theorem for Zermelo-Fraenkel Set Theory with the Axiom of Dependent Choice