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A solution for scattered order types of a problem of Hagendorf

A solution for scattered order types of a problem of Hagendorf

asked if every order type φ having the following two properties of additively indecomposable ordinals was the order type of an ordinal.Call φ Hagendorf if (i) it is strictly indecomposable to the right, i.e., if φ = φ + θ, then φ can be embedded in θ but not in …