Classes of Polish Spaces Under Effective Borel Isomorphism

The author studies the equivalence classes under $Delta11$ 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 $Delta11$-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.