Publications by Alberto Marcone


  1. Alberto Marcone and Andrea Volpi, Reverse mathematics and dimension of posets, submitted. arXiv:2603.18759

  2. Garrett Ervin, Alberto Marcone, and Thilo Weinert, Untranscendable order types, submitted. arXiv:2602.24285

  3. Alberto Marcone and Gian Marco Osso, The reverse mathematics of Brooks’ theorem, submitted. arXiv:2601.04001

  4. Riccardo Camerlo, Alberto Marcone, and Luca Motto Ros, Isometry groups of Polish ultrametric space , submitted, arXiv:2508.08480

  5. Andrea Brun, Alberto Marcone and Guido Gherardi, Computability of a Whitney Extension, submitted, arXiv:2507.02113

  6. Alberto Marcone, Antonio Montalbán, and Andrea Volpi, The barrier Ramsey theorem, Transactions of the American Mathematical Society, to appear. arXiv:2505.02544

  7. Vittorio Cipriani, Alberto Marcone, and Luca San Mauro, On the learning power of Friedman-Stanley jumps, submitted. arXiv:2501.12846

  8. Steffen Lempp, Alberto Marcone, and Manlio Valenti, Chains and antichains in the Weihrauch lattice, submitted. arXiv:2411.07792

  9. Alberto Marcone and Gian Marco Osso, The Galvin-Prikry theorem in the Weihrauch lattice, submitted. arXiv:2410.06928

  10. Uri Andrews, Steffen Lempp, Alberto Marcone, Joseph S. Miller, and Manlio Valenti, A jump operator on the Weihrauch degrees, Computability 14 (2025), 73-94. arXiv:2402.13163

  11. Martina Iannella, Alberto Marcone, Luca Motto Ros ,and Vadim Weinstein, Piecewise convex embeddability on linear orders, Annals of Pure and Applied Logic 176 (2025), article 103581. arXiv:2312.01198

  12. Martina Iannella, Alberto Marcone, Luca Motto Ros ,and Vadim Weinstein, Convex embeddability and knot theory, Transactions of the American Mathematical Society 378 (2025), 2745–2796. arXiv:2309.09910

  13. Anton Freund, Alberto Marcone, Fedor Pakhomov, and Giovanni Soldà, Provable better quasi orders, Notre Dame Journal of Formal Logic 66 (2025), 175-178. arXiv:2305.01066

  14. Vittorio Cipriani, Alberto Marcone, and Manlio Valenti, The Weihrauch lattice at the level of Π11-CA0: the Cantor-Bendixson theorem, The Journal of Symbolic Logic 90 (2025), 752-790. arXiv:2210.15556

  15. Alberto Marcone and Manlio Valenti, Effective aspects of Hausdorff and Fourier dimension, Computability 11 (2022), 299-333. arXiv:2108.06941

  16. Marta Fiori-Carones, Alberto Marcone, Paul Shafer and Giovanni Soldà, (Extra)ordinary equivalences with the ascending/descending sequence principle, The Journal of Symbolic Logic 89 (2024), 262-307. arXiv:2107.02531

  17. Marta Fiori-Carones and Alberto Marcone, Uniquely orderable interval graphs, Discrete Mathematics, 345 (2022), article 112935. arXiv:2101.09111

  18. Alberto Marcone and Manlio Valenti, On the descriptive complexity of Salem sets, Fundamenta Mathematicae 257 (2022), 69-93. arXiv:2009.09888

  19. Alberto Marcone and Manlio Valenti, The open and clopen Ramsey theorems in the Weihrauch lattice, The Journal of Symbolic Logic, 86 (2021), 316-351. arXiv:2003.04245

  20. Marta Fiori-Carones and Alberto Marcone, To reorient is easier than to orient: an on-line algorithm for reorientation of graphs, Computability 10 (2021), 215-233. arXiv:1910.01879

  21. Takayuki Kihara, Alberto Marcone, and Arno Pauly, Searching for an analogue of ATR0 in the Weihrauch lattice, The Journal of Symbolic Logic, 85 (2020), 1006-1043. arXiv:1812.01549

  22. Riccardo Camerlo, Alberto Marcone, and Luca Motto Ros, Polish metric spaces with fixed distance set, Annals of Pure and Applied Logic 171 (2020) article 102832. arXiv:1809.06588

  23. Guido Gherardi, Alberto Marcone, and Arno Pauly, Projection operators in the Weihrauch lattice, Computability 8 (2019) 281-304, arXiv:1805.12026

  24. Alberto Marcone, The reverse mathematics of wqos and bqos, in: Well quasi-orders in computation, logic, language and reasoning (P. Schuster, M. Seisenberger, A. Weiermann, eds.), Trends in Logic, Vol. 53, Springer, 2020, pp. 189--219. arXiv:1707.08365

  25. Riccardo Camerlo, Raphaël Carroy, and Alberto Marcone, Linear orders: when embeddability and epimorphism agree, Journal of Mathematical Logic 19.01 (2019). arXiv:1701.02020

  26. Giovanna D'Agostino and Alberto Marcone, The logic of the reverse mathematics zoo, Mathematical Structures in Computer Science 28 (2018), 412-428. arXiv:1512.08035

  27. Emanuele Frittaion, Matthew Hendtlass, Alberto Marcone, Paul Shafer e Jeroen Van der Meeren, Reverse mathematics, well-quasi-orders, and Noetherian spaces, Archive for Mathematical Logic 55 (2016), 431-459. arXiv:1504.07452

  28. Riccardo Camerlo, Alberto Marcone, and Luca Motto Ros, On isometry and isometric embeddability between metric and ultrametric Polish spaces, Advances in Mathematics 329 (2018) 1231–1284. arXiv:1412.6659

  29. Riccardo Camerlo, Raphaël Carroy, and Alberto Marcone, Epimorphisms between linear orders, Order 32 (2015), 387-400. arXiv:1403.2158

  30. Emanuele Frittaion and Alberto Marcone, Reverse Mathematics and initial intervals, Annals of Pure and Applied Logic 165 (2014), 858–879. arXiv:1303.2926

  31. Emanuele Frittaion and Alberto Marcone, Linear extensions of partial orders and Reverse Mathematics, MLQ Mathematical Logic Quarterly 58 (2012), 417-423. arXiv:1203.5207

  32. Alberto Marcone, Antonio Montalbán and Richard Shore, Computing maximal chains, Archive for Mathematical Logic 51 (2012), 651-660. arXiv:1201.4408

  33. Vasco Brattka, Guido Gherardi, and Alberto Marcone, The Bolzano-Weierstrass Theorem is the Jump of Weak König's Lemma, , Annals of Pure and Applied Logic 163 (2012) 623-655. Vasco Brattka, Andrea Cettolo, Guido Gherardi, Alberto Marcone, and Matthias Schröder, Addendum, Annals of Pure and Applied Logic 168 (2017), 1605-1608. arXiv:1101.0792

  34. Alberto Marcone and Richard Shore, The maximal linear extension theorem in second order arithmetic, Archive for Mathematical Logic 50 (2011), 543-564. arXiv:1009.1528

  35. Riccardo Camerlo, Alberto Marcone, and Luca Motto Ros, Invariantly universal analytic quasi-orders, Transactions of the American Mathematical Society 365 (2013) 1901-1931. arXiv:1003.4932

  36. Alberto Marcone and Antonio Montalbán, The Veblen functions for computability theorists, The Journal of Symbolic Logic 76 (2011), 575-602. arXiv:0910.5442

  37. Guido Gherardi and Alberto Marcone, How incomputable is the separable Hahn-Banach theorem?, Notre Dame Journal of Formal Logic 50 (2009) 393-425. arXiv:0808.1663 (extended abstract in Electronic Notes in Theoretical Computer Science 221 (2008) (Proceedings of the Fifth International Conference on Computability and Complexity in Analysis (CCA 2008)), 85-102).

  38. Alberto Marcone and Antonio Montalbán, On Fraïssé’s conjecture for linear orders of finite Hausdorff rank, Annals of Pure and Applied Logic 160 (2009) 355-367. pdf file

  39. Riccardo Camerlo and Alberto Marcone, Coloring linear orders with Rado's partial order, MLQ Mathematical Logic Quarterly 53 (2007) 301-305. pdf file

  40. Alberto Marcone, Interval orders and reverse mathematics, Notre Dame Journal of Formal Logic 48 (2007), 425-448. arXiv:math/0609022

  41. Alberto Marcone, Complexity of sets and binary relations in continuum theory: a survey, in: Set Theory. Centre de Recerca Matemàtica Barcelona, 2003-2004, (J. Bagaria and S. Todorcevic, eds.), Trends in Mathematics, Birkhäuser, 2006, pp.121-147. pdf file

  42. Udayan B. Darji and Alberto Marcone, Complexity of curves, Fundamenta Mathematicae 182 (2004) 79-93. pdf file

  43. Peter Cholak, Alberto Marcone, and Reed Solomon Reverse mathematics and the equivalence of definitions for well and better quasi-orders, The Journal of Symbolic Logic 69 (2004) 683-712. pdf file (on Cholak's site).

  44. Christian Rosendal and Alberto Marcone, The complexity of continuous embeddability between dendrites, The Journal of Symbolic Logic 69 (2004) 663-673. pdf file

  45. Riccardo Camerlo, Udayan B. Darji, and Alberto Marcone, Classification problems in continuum theory, Transactions of the American Mathematical Society 357 (2005) 4301-4328. pdf file

  46. Alberto Marcone, WQO and BQO theory in subsystems of second order arithmetic, in: Reverse Mathematics 2001 (S.G. Simpson, Ed.), Lecture Notes in Logic 21, Association for Symbolic Logic, 2005, pp. 303-330. pdf file

  47. Alberto Marcone, Fine analysis of the quasi-orderings on the power set, Order 18 (2001) 339-347.

  48. Alessandro Andretta and Alberto Marcone, Definability in function spaces, (Real Analysis Exchange 26 (2000/01) 285-308. pdf is open access on project Euclid

  49. Alessandro Andretta and Alberto Marcone, Pointwise convergence and the Wadge hierarchy, Commentationes Mathematicae Universitatis Carolinae 42 (2001) 159-172.

  50. Alessandro Andretta and Alberto Marcone, Projective sets and ordinary differential equations, Transactions of the American Mathematical Society 353 (2001) 41-76.

  51. Camillo Costantini and Alberto Marcone, Extensions of functions which preserve the continuity on the original domain, Topology and its Applications 103 (2000) 131-153.

  52. Alberto Marcone, Franco Parlamento, and Alberto Policriti, Finite families with few symmetric differences, Proceedings of the American Mathematical Society 127 (1999) 835-845.

  53. Mariagnese Giusto and Alberto Marcone, Lebesgue numbers and Atsuji spaces in subsystems of second-order arithmetic, Archive for Mathematical Logic 37 (1998) 343-362. arXiv:math/9602203

  54. Alessandro Andretta and Alberto Marcone, Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension, Fundamenta Mathematicae 153 (1997) 157-190. arXiv:math/9408204

  55. Alberto Marcone, On the logical strength of Nash-Williams' theorem on transfinite sequences, in: Logic: from Foundations to Applications; European logic colloquium (W. Hodges, M. Hyland, C. Steinhorn and J. Truss, Eds.), Clarendon Press, 1996, pp. 327-351. arXiv:math/9408204

  56. Alberto Marcone, The set of better quasi orderings is $\Pi^1_2$-complete, Mathematical Logic Quarterly 41 (1995) 373-383. arXiv:math/9405207

  57. Alberto Marcone, Foundations of bqo theory, Transactions of the American Mathematical Society 345 (1994) 641-660.

  58. Alberto Marcone, Borel quasi-orderings in subsystems of second-order arithmetic, Annals of Pure and Applied Logic 54 (1991) 265-291.

  59. Alberto Marcone, Theory of sets and classes and systems used in reverse mathematics, Rendiconti del seminario matematico dell'Università e del Politecnico di Torino 46 (1988) 189-215.


Papers popularizing my areas of research (in Italian)


  1. Guido Gherardi and Alberto Marcone, Le direzioni della logica in Italia: la reverse mathematics e l'analisi computazionale, in: Le direzioni della ricerca logica in Italia, vol. 2 (H Hosni, G. Lolli, C. Toffalori, Eds.), ETS, 2018, pp. 295-332.

  2. Alberto Marcone, Equivalenze tra teoremi: il programma di ricerca della reverse mathematics, La Matematica nella Società e nella Cultura, Rivista dell’Unione Matematica Italiana, Serie I II (2009), 101-126.

  3. Alberto Marcone, La reverse mathematics e i fondamenti della matematica, in: Conferenze e Seminari 2001-2002 (E. Gallo, L. Giacardi, O. Robutti, Eds.), Associazione Subalpina Mathesis e Seminario di Storia delle Matematiche “T. Viola”, 2002, pp. 169-178.

  4. Alberto Marcone, Quali assiomi per la matematica? Dall'assioma delle parallele alla reverse mathematics, in: Conferenze e Seminari 1993--1994 (E. Gallo, L. Giacardi, F. Pastrone, Eds.), Associazione Subalpina Mathesis e Seminario di Storia delle Matematiche “T. Viola”, 1994, pp. 201-211.