Domains via Graphs

This paper provides a concrete and simple introduction to two pillars of domain theory : (1) solving recursive domain equations, and (2) universal and saturated domains. Our exposition combines Larsen and Winskel's idea on solving domain equations using information systems with Girard's idea of stable domain theory in the form of coherence spacest or graphs. Detailed constructions are given for universal and even homogeneous objects in two categories of graphs: one representing binary complete, prime algebraic domains with complete primes covering the bottom; the other representing w-algebraic, prime algebraic lattices. The back- and-forth argument in model theory helps to enlighten the constructions.