Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The authors explore the possibility of using different condition coherence, which has its origin in topology and logic. In particular, they concentrate on posets with principal ideas that are algebraic lattices and with coherent topologies. These form a Cartesian closed category has fixed points for domain equations. It is shown that a universal domain exists. A categorical treatment of the construction of this domain is provided, and its relationship to other applications discussed.