In this paper it is shown that the global statement that the dominating number for κ is less than 2κ for all regular κ, is internally consistent, given the existence of 0#. The possible range of values for the dominating number for κ and 2κ which may be simultaneously true in an inner model is also explored.
"An inner model for global domination." J. Symbolic Logic 74 (1) 251 - 264, March 2009. https://doi.org/10.2178/jsl/1231082311