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- Luca Motto Ros
- J. Symb. Log.
- 2013

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 α -measurable functions (for every fixed 1 ď α ă ω1). Moreover, we present some results concerning those Borel functions… (More)

- Luca Motto Ros
- J. Symb. Log.
- 2009

We show that if F is any “well-behaved” subset of the Borel functions and we assume the Axiom of Determinacy then the hierarchy of degrees on P(ωω) induced by F turns out to look like the Wadge hierarchy (which is the special case where F is the set of continuous functions).

- Luca Motto Ros
- Math. Log. Q.
- 2011

We present a general way of defining various reduction games on ω which “represent” corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for functions which are pointwise limit of certain sequences of functions and for Γ-measurable functions. These games turn out to be… (More)

- Sy-David Friedman, Luca Motto Ros
- J. Symb. Log.
- 2011

We give a new characterization of the Baire class 1 functions (defined on an ultrametric space) by proving that they are exactly the pointwise limits of sequences of full functions, which are particularly simple Lipschitz functions. Moreover we highlight the link between the two classical stratifications of the Borel functions by showing that the Baire… (More)

- Luca Motto Ros, Philipp Schlicht, Victor L. Selivanov
- Mathematical Structures in Computer Science
- 2015

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)

- Luca Motto Ros
- J. Symb. Log.
- 2010

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)

- Luca Motto Ros
- Ann. Pure Appl. Logic
- 2013

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)

- Yurii Khomskii, Giorgio Laguzzi, +20 authors Daisuke Ikegami
- 2015

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 recent developments in this area. This compilation is based on the open questions raised in the talks and the discussions during… (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)