**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.*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. (italiano)

**Descriptive Set
Theory**

*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

*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.

**WQO
and BQO theory**

**Computable
Analysis**

*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).

**Other**

*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).