Classes of Polish spaces under effective Borel isomorphism

The author studies the equivalence classes under \Delta^1_1 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of \Delta^1_1-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.