**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, to appear**.**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*, (with Riccardo Camerlo and Raphaël Carroy), Journal of Mathematical Logic*Linear orders: when embeddability and epimorphism agree***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**Π*^{1}_{1}*-CA*_{0}*: 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*ATR_{0}*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.