Luca Motto Ros

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In [8] we have considered a wide class of " well-behaved " reducibil-ities for sets of reals. In this paper we continue with the study of Borel re-ducibilities 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(More)
The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well-ordered), but for many other natural non-zero-dimensional 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(More)
We show that if κ is a weakly compact cardinal then the embed-dability relation on (generalized) trees of size κ is invariantly universal. This means that for every analytic quasi-order on the generalized Cantor space κ 2 there is an L κ + κ-sentence ϕ such that the embeddability relation on its models of size κ, which are all trees, is Borel bireducible(More)
The goal of this survey paper is to provide a list of open problems in the burgeoning research area of generalized Baire spaces. This survey paper is the output of two workshops on generalized Baire spaces, the first held in Amsterdam in 2014, and the second in Hamburg in 2015. During both meetings, a group of set theorists met and presented some of the(More)
We give a full description of the structure under inclusion of all finite level Borel classes of functions, and provide an elementary proof of the well-known fact that not every Borel function can be written as a countable union of Σ 0 α-measurable functions (for every fixed 1 ď α ă ω 1). Moreover , we present some results concerning those Borel functions(More)