Additively indecomposable ordinal

An additively indecomposable ordinal is a type of ordinal number that cannot be expressed as the sum of two smaller ordinals. In formal terms, an ordinal \(\alpha\) is considered additively indecomposable if, whenever \(\alpha = \beta + \gamma\) for some ordinals \(\beta\) and \(\gamma\), at least one of \(\beta\) or \(\gamma\) must be zero.