Publications by topic

Borel reducibility and classification

• Analytic equivalence relations and bi-embeddability, joint work with Sy-D. Friedman, Journal of Symbolic Logic 76 (2011), no. 1, 243-266 (24 pages).

• On the complexity of the relations of isomorphism and bi-embeddability, Proceedings of the American Mathematical Society 140 (2012), no. 1, 309-323 (15 pages).

• Invariantly universal analytic quasi-orders, joint work with Riccardo Camerlo and Alberto Marcone, Transactions of the American Mathematical Society 365 (2013), no. 4, 1901-1931 (31 pages).

• Can we classify complete metric spaces up to isometry?, Bollettino dell'Unione Matematica Italiana 10 (2017), no. 3, 369–410 (42 pages). It includes a section on generalized descriptive set theory.

• Universality of group embeddability, joint work with Filippo Calderoni, Proceedings of the American Mathematical Society 146 (2018), no. 4, 1765–1780 (16 pages).

• On isometry and isometric embeddability between metric and ultrametric Polish spaces, joint work with Riccardo Camerlo and Alberto Marcone, Advances in Mathematics 329 (2018), 1231–1284 (53 pages).

• Polish metric spaces with fixed distance set, joint work with Riccardo Camerlo and Alberto Marcone, Annals of Pure and Applied Logic 171 (2020), no. 10, 102832 (25 pages).

• Anti-classification results for groups acting freely on the line, joint work with F. Calderoni, D. Marker and A. Shani, Advances in Mathematics 418 (2023), Paper No. 108938 (45 pages).

• Classification problems from the descriptive set theoretical perspective, accepted for publication in the collection Research Trends in Contemporary Logic, edited by Melvin Fitting, Dov Gabbay, Massoud Pourmahdian, Adrian Rezus, and Ali Sadegh Daghighi (26 pages).

Generalized descriptive set theory

• The descriptive set-theoretical complexity of the embeddability relation on models of large size, Annals of Pure and Applied Logic 164 (2013), 1454-1492 (39 pages).

• The Hurewicz dichotomy for generalized Baire spaces, joint work with Philipp Lücke and Philipp Schlicht, Israel Journal of Mathematics 216 (2016), no. 2, 973–1022 (50 pages).

• Uncountable structures are not classifiable up to bi-embeddability, joint work with Heike Mildenberger and Filippo Calderoni, Journal of Mathematical Logic 20 (2020), no. 1, 2050001 (49 pages).

• A descriptive main gap theorem, joint with Francesco Mangraviti, Journal of Mathematical Logic 21 (2020), no. 1, 2050025 (40 pages).

• Souslin quasi-orders and bi-embeddability of uncountable structures, joint work with Alessandro Andretta, Memoirs of the American Mathematical Society 277 (2022), no. 1365 (196 pages).

• Generalized Polish spaces at regular uncountable cardinals, joint work with C. Agostini and P. Schlicht, Journal of the London Mathematical Society 108 (2023), no. 5, 1886–1929 (44 pages).

Decomposability and stratifications of Borel functions

• A new characterization of the Baire class 1 functions, Real Analysis Exchange 34 (2008/2009), no. 1, 29-48 (20 pages).

• A new proof of a theorem of Jayne and Rogers, joint work with Brian Semmes, Real Analysis Exchange 35 (2010), no. 1, 195-203 (9 pages).

• Game representations of classes of piecewise definable functions, Mathematical Logic Quarterly 57 (2011), no.1, 95-112 (18 pages).

• Some observations on "A new proof of a theorem of Jayne and Rogers", joint work with Miroslav Kačena and Brian Semmes, Real Analysis Exchange 38 (2012/2013), no. 1, 121-132 (12 pages).

• On the structure of finite level and omega-decomposable Borel functions, Journal of Symbolic Logic 78 (2013), no. 4, 1257-1287 (31 pages).

Wadge theory

• Borel-amenable reducibilities for sets of reals, Journal of Symbolic Logic 74 (2009), no. 1, 27-49 (23 pages).

• Baire reductions and good Borel reducibilities, Journal of Symbolic Logic 75 (2010), no. 1, 323-345 (23 pages).

• Beyond Borel-amenability: scales and superamenable reducibilities, Annals of Pure and Applied Logic 161 (2010), 829-836 (8 pages).

• Bad Wadge-like reducibilities on the Baire space, Fundamenta Mathematicae 224 (2014), no. 1, 67-95 (29 pages).

• Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces, joint work with Philipp Schlicht in: V. Brattka, H. Diener, and D. Spreen (Eds.), Logic, Computation, Hierarchies, Ontos Mathematical Logic 4, de Gruyter, Berlin, Boston, 2014, pp. 213-258 (46 pages).

• Wadge-like reducibilities on arbitrary quasi-Polish spaces, joint work with Philipp Schlicht and Victor Selivanov, Mathematical Structures in Computer Science 25 (2015), Special issue 08, 1705-1754 (50 pages).

• A classification of the Wadge hierarchies on zero-dimensional Polish spaces, joint work with R. Carroy and S. Scamperti, accepted for publication on the Journal of Symbolic Logic, 2023 (30 pages).