A Note on a Model of Synthetic Domain Theory Marcelo P. Fiore Giuseppe Rosolini LFCS, The King's Buildings DIMA, via Dodecaneso 35 Edinburgh EH9 3JZ 16146 Genova Scotland Italy Abstract A model of synthetic domain theory embedding the category omega-Cpo of omega-complete posets and omega-continuous functions as a reflective exponential ideal is introduced, and an internal characterisation of omega-Cpo within the model is presented.