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@inproceedings{NormannDefinabilityAR, title={Definability and reducibility in higher types over the reals}, author={Dag Normann} }

We consider sets CtR(σ) of total, continuous functionals of type σ over the reals. A subset A ⊆ CtR(σ) is reducible if A can be reduced to totality in one of the other spaces. We show that all Polish spaces are homeomorphic to a reducible subset of R → R and that the class of reducible sets is closed under the formation of function spaces and some… CONTINUE READING