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trees/dt/dt-0067.tree
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\import{dt-macros}
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\author{liamoc}
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\title{The Plotkin powerdomain}
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\p{As before, let #{X, Y \in \mathcal{P}_f^\ast(\compact{A})} be finite, non-empty sets of [compact elements](dt-003U) of a [Scott domain](dt-004G) #{A}. The \em{Plotkin powerdomain} construction is based on the following \em{preorder}, simply combining the orderings from the [Hoare](dt-0061) and [Smyth](dt-0064) constructions:
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\p{As before, let #{X, Y \in \mathcal{P}_f^\ast(\compact{A})} be finite, non-empty sets of [compact elements](dt-003U) of a [Scott domain](dt-004G) #{A}. The \em{Plotkin powerdomain} construction is based on the following [preorder](dm-000V), simply combining the orderings from the [Hoare](dt-0061) and [Smyth](dt-0064) constructions:
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##{
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X \preceq_P Y\quad \text{iff}\quad X \preceq_H Y \land X \preceq_S Y
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}