Free modal lattices via Priestley duality (Q1604799)

A modal lattice \(L\) is an algebra \(L=(L;\vee, \wedge,j,0, 1)\), where \((L;\vee, \wedge,0,1)\) is a bounded distributive lattice and \(j\) is a unary operation satisfying the following identities: (i) \(x\leq j(x)\), (ii) \(j(x)= j(j(x))\) and (iii) \(j(x\wedge y)=j(x) \wedge j(y)\). The author describes (1) the dual spaces of modal lattices in the Priestley duality and (2) constructs the dual spaces of free modal lattices.