Kanda A., Park D. (1979) When are two effectively given domains identical?. In: Weihrauch K. (eds) Theoretical Computer Science 4th GI Conference. Lecture Notes in Computer Science, vol 67. Springer, Berlin, Heidelberg
In this paper, we will observe that the notion of computability in an effectively given domain is dependent on the indexing of its basis. This indicates that we cannot identify two effectively given domains just because they are order isomorphic. We propose a suitable notion of effective isomorphism to compensate for this deficiency. Also we show that, for every recursion domain equation, there is an effectively given domain which is an initial solution to within effective isomorphism.