Countable partition ordinals

The structure of ordinals of the form ω ω β for countable β is studied. The main result is: Theorem 1 lt; ω 1 is the sum of one or two indecomposable ordinals, then ω ω β → ( ω ω β , 3 ) 2 . an example is given to show that α → ( α , 3 ) 2 need not imply α → ( α , n ) 2 for all n < ω .