Irreducibility in generalized power series

Abstract

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 $\alpha$ of non-additively principal Cantor degree for which $K(({\mathbb{R}}^{\le 0}))$ admits irreducibles of order type $\alpha$ far beyond $\alpha ={\omega }^2$ and $\alpha ={\omega }^3$ known prior to this work.