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 ω ω 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 ω ω / U is greater than max { b , g } . The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.