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Let $(P, \le)$ be a poset set such that $$ \forall a, b, c \in P: b \ge a \le c \implies \exists d \in P: b \le d \ge c. $$ I am looking for literature where such confluent partial orders are studied.

Let $(P, \le)$ be a poset set such that $$ \forall a, b, c \in P: b \ge a \le c \implies \exists d \in P: b \le d \ge c. $$ I am looking for literature where such confluent partial orders are studied.

Let $(P, \le)$ be a poset such that $$ \forall a, b, c \in P: b \ge a \le c \implies \exists d \in P: b \le d \ge c. $$ I am looking for literature where such confluent partial orders are studied.

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Confluent partial orders

Let $(P, \le)$ be a poset set such that $$ \forall a, b, c \in P: b \ge a \le c \implies \exists d \in P: b \le d \ge c. $$ I am looking for literature where such confluent partial orders are studied.