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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