Decomposition of infinite labeled 2-structures

Abstract

We generalize the decomposition theorem for finite 2-structures (from Ehrenfeucht and Rozenberg, Theoret. Comput. Sci. 70 (1990)) to infinite labeled 2-structures. It is shown that if an infinite labeled 2-structure g has at least one maximal prime clan, then its maximal prime clans form a partition of the domain of g, and the quotient w.r.t. this partition is linear, complete or primitive. Also, we show that the infinite primitive labeled 2-structures are upward hereditary, i.e., if h is a primitive substructure of a primitive g, then h can be extended to a primitive substructure h′ of g by adding one or two nodes to h.