A Classification of Simple Limits of Splitting Interval Algebras

LetAbe a unital simple limit of finite direct sums of sub-homogeneous interval algebras of a certain type (cf. Definition 1.1). It is proved thatAcan be classified by the scaled ordered groupK0(A), the simplexT(A), and the canonical pairing between them. It is also shown thatK0(A) might fail to have the Riesz decomposition property.