Covering the Baire space by families which are not finitely dominating

It is consistent (relative to ZFC) that each union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.