Irreducibility in generalized power series

A classical tool in the study of real closed fields are the fields $K((G))$ of generalized power series (i.e., formal sums with well-ordered support) with coefficients in a field K of characteristic 0 and exponents in an ordered abelian group G. In this paper we enlarge the family of ordinals α of non-additively principal Cantor degree for which K((R≤ 0)) admits irreducibles of order type α far beyond α=ω² and α = ω³ known prior to this work.