Publications by Alberto Marcone
Reverse Mathematics and Computable Mathematics
The reverse mathematics of wqos and bqos, to appear in: Well quasi-orders in computation, logic, language and reasoning (P. Schuster, M. Seisenberger, A. Weiermann, eds.), Trends in Logic, Springer. arXiv:1707.08365
Reverse mathematics, well-quasi-orders, and Noetherian spaces, Archive for Mathematical Logic 55 (2016), 431-459 (with E. Frittaion, M. Hendtlass, P. Shafer e J. Van der Meeren). arXiv:1504.07452
Reverse Mathematics and initial intervals, Annals of Pure and Applied Logic 165 (2014), 858–879 (with E. Frittaion). arXiv:1303.2926
Linear extensions of partial orders and Reverse Mathematics, MLQ Mathematical Logic Quarterly 58 (2012), 417-423 (with E. Frittaion). arXiv:1203.5207
Computing maximal chains, Archive for Mathematical Logic 51 (2012), 651-660 (with A. Montalbán and R.A. Shore). arXiv:1201.4408
The maximal linear extension theorem in second order arithmetic, Archive for Mathematical Logic 50 (2011), 543-564 (with R.A. Shore). arXiv:1009.1528
The Veblen functions for computability theorists, The Journal of Symbolic Logic 76 (2011), 575-602 (with A. Montalbán). arXiv:0910.5442
On Fraïssé’s conjecture for linear orders of finite Hausdorff rank, Annals of Pure and Applied Logic 160 (2009) 355-367 (with A. Montalbán). 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, The Journal of Symbolic Logic 69 (2004) 683-712 (with P. Cholak and R. Solomon). 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, Archive for Mathematical Logic 37 (1998) 343-362 (with M. Giusto). 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
Polish metric spaces with fixed distance set, (with R. Camerlo and L. Motto Ros), submitted. arXiv:1809.06588
Linear orders: when embeddability and epimorphism agree, (with R. Camerlo and R. Carroy), submitted. arXiv:1701.02020
On isometry and isometric embeddability between metric and ultrametric Polish spaces, Advances in Mathematics 329 (2018) 1231–1284 (with R. Camerlo and L. Motto Ros). arXiv:1412.6659
Invariantly universal analytic quasi-orders, Transactions of the American Mathematical Society 365 (2013) 1901-1931 (with R. Camerlo and L. Motto Ros). arXiv:1003.4932
Coloring linear orders with Rado's partial order, MLQ Mathematical Logic Quarterly 53 (2007) 301-305 (with R.Camerlo). 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, Fundamenta Mathematicae 182 (2004) 79-93 (with U.B. Darji). pdf file
The complexity of continuous embeddability between dendrites, The Journal of Symbolic Logic 69 (2004) 663-673 (with C. Rosendal). pdf file
Classification problems in continuum theory, Transactions of the American Mathematical Society 357 (2005) 4301-4328 (with R. Camerlo and U.B. Darji). pdf file
Definability in function spaces, Real Analysis Exchange 26 (2000/01) 285-308 (with A. Andretta). pdf is open access on project Euclid
Pointwise convergence and the Wadge hierarchy, Commentationes Mathematicae Universitatis Carolinae 42 (2001) 159-172 (with A. Andretta).
Projective sets and ordinary differential equations, Transactions of the American Mathematical Society 353 (2001) 41-76 (with A. Andretta).
Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension, Fundamenta Mathematicae 153 (1997) 157-190 (with A. Andretta). 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 R. Camerlo and R. 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.
Projection operators in the Weihrauch lattice, (with G. Gherardi and A. Pauly), submitted. arXiv:1805.12026
The Bolzano-Weierstrass Theorem is the Jump of Weak König's Lemma, Annals of Pure and Applied Logic 163 (2012) 623-655 (with V. Brattka and G. Gherardi). Addendum, Annals of Pure and Applied Logic 168 (2017), 1605-1608 (with V. Brattka, A. Cettolo, G. Gherardi e M. Schröder). arXiv:1101.0792
How incomputable is the separable Hahn-Banach theorem?, Notre Dame Journal of Formal Logic 50 (2009) 393-425 (with G. Gherardi). 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).
The logic of the reverse mathematics zoo, Mathematical Structures in Computer Science 28 (2018), 412-428 (with G. D'Agostino). arXiv:1512.08035
Extensions of functions which preserve the continuity on the original domain, Topology and its Applications 103 (2000) 131-153 (with C. Costantini).
Finite families with few symmetric differences, Proceedings of the American Mathematical Society 127 (1999) 835-845 (with. F. Parlamento and A. Policriti).
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 G. 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.