**Research**

**Current main interests:**

**-** mathematical logic

**-** descriptive set theory

**-** real analysis and measure theory

**-** automaton theory

**-** wqo and bqo theory

**-** modal logic, proof theory, and their interactions with other areas of mathematics

**Publications**

· (with A.S. Kechris) *Countable
structures with a fixed group of automorphisms*, **Israel Journal of
Mathematics** 117 (2000), 105-124.

· (with S. Gao) *The completeness of the
isomorphism relation for countable Boolean algebras*, **Transactions of the
American Mathematical Society** 353 (2001), 491-518.

· (with A. Andretta and G. Hjorth) *Conjugacy
equivalence relation on subgroups*, **Fundamenta Mathematicae** 167
(2001), 189-212.

· *The relation of recursive isomorphism for
countable structures*, **The Journal of Symbolic Logic** 67 (2002),
879-895.

· *Matematica e problemi di
classificazione*, in **Conferenze e Seminari 2001-2002 dell’Associazione
Subalpina Mathesis** (edited by E. Gallo, L. Giacardi, O. Robutti), Mathesis
2002, 159-168.

· (with U.B. Darji) *Construction
of Borel inseparabile coanalytic sets*, **Real Analysis Exchange** 28
(2002/03), 163-180.

· *Classification problems in algebra and
topology*, in **Classical and New Paradigms of Computation and their
Complexity Hierarchies** (edited by B. Löwe, B. Piwinger, T. Räsch), Kluwer
2004, 61-75.

· *Continua and their σ-ideals*, **Topology and its Applications** 150
(2005), 1-18.

· (with A. Andretta) *The use of complexity
hierarchies in descriptive set theory and automata theory*, **Task Quarterly** 9 (2005), 337-356.

· *Universal analytic preorders arising from
surjective functions*, **Fundamenta Mathematicae** 187 (2005), 193-212.

· *Universality of embeddability relations for
coloured total orders*, **Order** 22 (2005), 289-300.

· (with U.B. Darji and A. Marcone) *Classification
problems in continuum theory*, **Transactions of the American Mathematical
Society** 357 (2005), 4301-4328.

· *The additivity of Hilbert cube under
embeddability*, **Atti del Seminario Matematico e Fisico
dell’Università di Modena e Reggio Emilia** 53 (2005), 13-16.

· (with A. Marcone) *Coloring linear orders with Rado's partial order*, **Mathematical Logic Quarterly** 53 (2007), 301-305.

· *Finiteness axioms on fragments of intuitionistic set theory*, **Notre Dame Journal of Formal Logic** 48 (2007), 473-488.

· *Characterising quotients of projective Fraïssé limits*, **Topology and its Applications** 157 (2010), 1980-1989.

· *Dendrites as Polish structures*, **Proceedings of the American Mathematical Society** 139 (2011), 2217-2225.

· (with A. Andretta) *The descriptive set theory of the Lebesgue density theorem*, **Advances in Mathematics** 234 (2013), 1-42.

· (with A. Marcone and L. Motto Ros) *Invariantly universal analytic quasi-orders*, **Transactions of the American Mathematical Society** 365 (2013), 1901-1931.

· *Complete sequences of coanalytic sets*, **Fundamenta Mathematicae** 224 (2014), 1-16.

· (with D. Bazzanella) *The class of the exceptional sets for a general asymptotic formula*, **Functiones et Approximatio Commentarii Mathematici** 51 (2014), 347-362.

· (with R. Carroy and A. Marcone) *Epimorphisms between linear orders*, **Order** 32 (2015), 387-400. Erratum, **Order** 33 (2016), 187.

· (with G. Basso) *Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits*, to appear in Mathematica Slovaca.

· (with J. Duparc) *Some remarks on Baire's grand theorem*, to appear in Archive for Mathematical Logic.

· (with A. Marcone and L. Motto Ros) *On isometry and isometric embeddability between ultrametric Polish spaces*, preprint.

· (with A. Andretta and C. Costantini) *Lebesgue density and exceptional points*, preprint.

· (with R. Carroy and A. Marcone) *Linear orders: when embeddability and epimorphism agree*, preprint.

· (with A. Andretta) *Analytic sets of reals and the density function in the Cantor space*, preprint.

· *Continuous reducibility: functions versus relations*, preprint.

· (with G. Pistone and F. Rapallo) *Modal operators and toric ideals*, preprint.

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