Publications by Alberto Marcone

Reverse Mathematics and Computable Mathematics

• Reverse Mathematics and initial intervals, (with E. Frittaion), submitted. 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

• 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

• 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

• 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). 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

• 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).