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- 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(ω ω) induced by F turns out to look like the Wadge hierarchy (which is the special case where F is the set of continuous functions).

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
- 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… (More)

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

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)

- 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-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)

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

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

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)

- Luca Motto Ros, Philipp Schlicht
- Logic, Computation, Hierarchies
- 2014

We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and determine whether under suitable set-theoretical assumptions the induced degree-structures are well-behaved.

- Luca Motto Ros
- 2014

Tenure-track researcher (Ricercatore a tempo determinato di tipo B) at the University of Turin — Department of Mathematics, 15.09.2014 – today. • Italian national scientific qualification (" habilitation ") as associate professor in the sector 01/A1 – Mathematical logic, mathematics education and history of mathematics,

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