Publications

Preprints of my papers are available on arXiv. Go to this page to see my published papers arranged by category.

Refereed Journals

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

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

3. 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).

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

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

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

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

8. 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).

9. 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).

10. 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).

11. 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).

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

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

14. 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).

15. 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).

16. 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).

17. Can we classify complete metric spaces up to isometry?, Bollettino dell'Unione Matematica Italiana 10 (2017), no. 3, 369–410 (42 pages).

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

19. 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).

20. 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).

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

22. 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).

23. 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).

24. 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).

25. 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).

26. 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).

27. 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).

Preprints and papers in preparation

1. Convex embeddability and knot theory, joint work with M. Iannella, A. Marcone, and V. Weinstein, submitted, (46 pages).

2. Piecewise convex embeddability on linear orders, joint work with M. Iannella, A. Marcone, and V. Weinstein, submitted, (34 pages).

3. A classification of \Delta^0_2-functions and a boundness theorem, in preparation.

4. Generalized descriptive set theory under I0, joint work with Vincenzo Dimonte and Xianghui Shi, in preparation.

Others

1. Hierarchies of complexity for sets, functions, and binary relations, Habilitationsschrift (thesis for obtaining my German habilitation), Albert-Ludwigs-Universität Freiburg, 2014. The thesis consists of an introduction plus 10 of my papers. All of them may be found here, together with some other material related to my Habilitation procedure.

2. General reducibilities for sets of reals, PhD thesis, Polytechnic of Turin, 2007 (thesis advisors: A. Andretta and R. Camerlo).

3. Metodi effettivi in teoria degli insiemi: la topologia di Gandy-Harrington, degree thesis, University of Turin, 2003 (thesis advisor: A. Andretta).

Slides of some talks

• Here are the slides of my talk at the online Paris-Lyon Logic seminar (september 2019) concerning anti-classification results for ordered groups (joint work with Filippo Calderoni, David Marker and Assaf Shani).

• Here are the slides of my talk at the Fifth Workshop on Generalised Baire Spaces held in Bristol (february 2020) concerning a descriptive version of Shelah's Main Gap Theorem (joint work with F. Mangraviti).

• Here are the slides of my talk at the 15th International Luminy Workshop in Set Theory held at CIRM Luminy (September 2019) concerning generalized Polish spaces for arbitrary infinite cardinals (partially joint work with Claudio Agostini, Philipp Schlicht, and others).

• Here are the slides of my talk at the conference "Set theory today: A conference in honor of Georg Cantor" held in Vienna (September 2018) concerning generalized descriptive set theory at uncountable cardinals of countable cofinality (joint work with Vincenzo Dimonte).

• Here are the slides of my talk at the SGSLPS 2017 Spring meeting “Borel Reducibility of Equivalence Relations” (May 2017) concerning some useful variants of Borel reducibility.

• Here are the slides (part 1 and part 2) of a tutorial I gave at the Bonn set theory workshop "Generalized Baire spaces" (September 2016) explaining how generalized descriptive set theory can be used to tackle classification problems for uncountable structures and non-separable spaces.

• Here are the slides of my talk at the "XX Congresso dell'Unione Matematica Italiana" (September 2015) concerning the classification of locally compact Polish ultrametric spaces up to isomorphism and bi-embeddability (joint work with Riccardo Camerlo and Alberto Marcone).

• Here are the slides of my talk at the "Amsterdam Workshop on Set Theory 2014" (November 2014) concerning the generalization of the Hurewicz dichotomy to the context of generalized descriptive set theory (joint work with Philipp Luecke and Philipp Schlicht).

• Here are the slides of my talk at the meeting "Set Theory" held in Oberwolfach (January 2014) concerning the descriptive set-theoretical complexity of the embeddability relation on uncountable models. This is a continuation of the work presented at the Logic Colloquium 2011 in Barcelona and is partially joint work with Alessandro Andretta and Heike Mildenberger.

• Here are the slides of my talk at the "Descriptive Set Theory in Paris" meeting (December 2013) concerning Lipschitz and uniformly continuous reducibilities on arbitrary ultrametric Polish spaces (partially joint work with P. Schlicht).

• Here are the slides of my talk at the Dagstuhl seminar "Duality in Computer Science" (August 2013) concerning Wadge-like reducibilities on arbitrary quasi-Polish spaces (joint work with Philipp Schlicht and Victor Selivanov).

• Here are the slides of my talk at the "Descriptive Set Theory in Paris" meeting (December 2012) concerning the structure of finite level and \omega-decomposable Borel functions.

• Here are the slides of my talk in the Set Theory special session of the Logic Colloquium 2011 held in Barcelona (July 2011) concerning the universality of the relation of embeddability among models of size a weakly compact cardinal.

• Here are the slides of my talk at the KGRC of Vienna (January 2010) concerning the relations of isomorphism and bi-embeddability.

• Here are the slides of my talk at the "ESI workshop on large cardinals and descriptive set theory" held in Vienna (June 2009) concerning (partial results on) invariantly universal analytic quasi-orders (partially joint work with Sy D. Friedman and Riccardo Camerlo).

• Here are the slides of my talk at the "Descriptive Set Theory in Paris" meeting (December 2008) concerning analytic equivalence relations and bi-embeddability (joint work with Sy D. Friedman).

• Here are the slides of my talk in Amsterdam (August 2007) concerning Borel reducibilities for sets of reals (generalizations of the Wadge structure).