Domains via graphs
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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 spaces, 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 representingw-algebraic, prime algebraic lattices. The back-and-forth argument in model theory helps to enlighten the constructions.
Keywordsdomain theory category theory graph theory universal objects recursive domain equations coherence spaces stable domains the back-and-forth argument
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