Publications by Alberto Marcone
Reverse Mathematics and Computable Mathematics
To reorient is easier than to orient: an on-line algorithm for reorientation of graphs, (with Marta Fiori-Carones), to appear in Computability. 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
On the descriptive complexity of Salem sets, (with Manlio Valenti), submitted. 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.
The open and clopen Ramsey theorems in the Weihrauch lattice, (with Manlio Valenti), to appear in The Journal of Symbolic Logic. 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).
Uniquely orderable interval graphs, (with Marta Fiori-Carones), submitted, 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.