Countable partition ordinals

Annals of Pure and Applied Logic 161 (10):1195-1215 (2010)
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Abstract

The structure of ordinals of the form ωωβ for countable β is studied. The main result is:Theorem 1If β<ω1 is the sum of one or two indecomposable ordinals, thenωωβ→2. Also an example is given to show that α→2 need not imply α→2 for all n<ω

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10.1016/j.apal.2009.12.007

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An ordinal partition avoiding pentagrams.Jean A. Larson - 2000 - Journal of Symbolic Logic 65 (3):969-978.

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