Luca Motto Ros

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The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well-ordered), but for many other natural non-zerodimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called ∆ 0 α-reductions, and try to find for various natural topological(More)
In [8] we have considered a wide class of “well-behaved” reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [8] allowing to deal with a larger class of notions of reduction(More)
We show that if κ is a weakly compact cardinal then the embeddability relation on (generalized) trees of size κ is invariantly universal. This means that for every analytic quasi-order on the generalized Cantor space 2 there is an Lκ+κsentence φ such that the embeddability relation on its models of size κ, which are all trees, is Borel bireducible (and, in(More)
We introduce the notion of an invariantly universal pair (S, E) where S is an analytic quasi-order and E ⊆ S ∩S is an analytic equivalence relation. This means that for any analytic quasi-order R there is a Borel set B invariant under E such that R is Borel equivalent to the restriction of S to B. We prove a general result giving a sufficient condition for(More)