Effective back-and-forth construction
= Effective back-and-forth construction
An effective back-and-forth construction alternately extends a finite <partial isomorphism of structures> to include the least unused domain and range elements, searching computably for a compatible extension. If extension always exists and its finite compatibility conditions are decidable, the union is a <computable isomorphism>. Decidable presentations of a <dense linear order without endpoints> provide a basic example.