In mathematics, a locally finite poset is a partially ordered set P such that for all x, y ∈ P, the interval [x, y] consists of finitely many elements.
Given a locally finite poset P we can define its incidence algebra.
Elements of the incidence algebra are functions ƒ that assign to each interval [x, y] of P a real number ƒ(x, y).
These functions form an associative algebra with a product defined by There is also a definition of incidence coalgebra.
In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime.