Definition. Poset [dm-0004]

Liam O'Connor

A partially ordered set, or poset for short, is a pair $(X, \sqsubseteq )$ of a set $X$ equipped with a partial order $(\sqsubseteq ) \subseteq X \times X$ .

Sometimes, when the ordering is arbitrary or clear from context, the set $X$ itself may be referred to as a poset.

Definition. Poset [dm-0004]

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Proof.

Example. The halting query [dt-000I]

Definition. Monotonicity [dt-000J]

Definition. Strictness [dt-000K]

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Exercise. [dt-000N]

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Exercise. [dt-000O]

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Exercise. [dt-000Q]

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