Publications by Alberto Marcone

Reverse Mathematics and Computable Mathematics

• Provable better quasi orders, (with Anton Freund, Fedor Pakhomov and Giovanni Soldà), submitted. arXiv:2305.01066

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

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

• 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

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

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

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

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

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

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

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

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

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

• 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

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

• 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

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

• 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.

• Descriptive Set Theory

• Piecewise convex embeddability on linear orders, (with Martina Iannella, Luca Motto Ros and Vadim Weinstein), submitted. arXiv:2312.01198

• Convex embeddability and knot theory, (with Martina Iannella, Luca Motto Ros and Vadim Weinstein), submitted. arXiv:2309.09910

• On the descriptive complexity of Salem sets, (with Manlio Valenti), Fundamenta Mathematicae 257 (2022), 69-93. arXiv:2009.09888

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

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

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

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

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

• 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

• Complexity of curves, (with Udayan B. Darji), Fundamenta Mathematicae 182 (2004) 79-93. pdf file

• The complexity of continuous embeddability between dendrites, (with Christian Rosendal), The Journal of Symbolic Logic 69 (2004) 663-673. pdf file

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

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

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

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

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

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

WQO and BQO theory

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

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

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

Computable Analysis and Weihrauch Lattice

• A jump operator on the Weihrauch degrees, (with Uri Andrews, Steffen Lempp, Joseph S. Miller and Manlio Valenti), submitted. arXiv:2402.13163

• The Weihrauch lattice at the level of Π¹₁-CA₀: the Cantor-Bendixson theorem, (with Vittorio Cipriani and Manlio Valenti), submitted. arXiv:2210.15556

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

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

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

• Projection operators in the Weihrauch lattice, (with Guido Gherardi and Arno Pauly), Computability 8 (2019) 281-304, arXiv:1805.12026

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

• How incomputable is the separable Hahn-Banach theorem?, (with Guido Gherardi), 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).

Other

• Uniquely orderable interval graphs, (with Marta Fiori-Carones), Discrete Mathematics, 345 (2022), article 112935. arXiv:2101.09111.

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

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

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

Papers popularizing my areas of research (in Italian)

• 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 (with Guido Gherardi).

• 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.

• 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.

• 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.