Definability and reducibility in higher types over the reals

@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