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
(f*g)(x,y):=\sumxf(x,z)g(z,y).
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.