Mauro Di Nasso

> HOME > CV > PAPERS > DIDATTICA > TESI > LINKS

PAPERS Idempotent ultrafilters without Zorn's Lemma (with E. Tachtsis), Proceedings of the America Mathematical Society, accepted for publication, arXiv:1701.03301 (2017) Ramsey properties of nonlinear Diophantine equations (with L. Luperi Baglini), Advances in Mathematics, accepted for publication, arXiv:1606.02056 (2016). Fermat-like equations that are not partition regular (with M. Riggio), Combinatorica, accepted for publication. (arXiv:1605.07527, 2016). High density piecewise syndeticity of product sets in amenable groups (with I. Goldbring, R. Jin, S. Leth, M.Lupini, K. Mahlburg), Journal of Symbolic Logic, vol. 81 (2016), pp. 1555-1562. Approximate polynomial structure in additively large sets (with I. Goldbring, R. Jin, S. Leth, M.Lupini, K. Mahlburg), Integers, vol. 16 (2016), A49, pp. 11. Hypernatural numbers as ultrafilters, chapter in "Nonstandard Analysis for the Working mathematician" (P.A. Loeb and M. Wolff, eds.), 2nd edition, Springer, 2015. A monad measure space for logarithmic density (with I. Goldbring, R. Jin, S. Leth, M.Lupini, K. Mahlburg), Monatshefte für Mathematik, vol. 181 (2016), pp. 577-599. Some applications of numerosities in measure theory (with V.Benci and E. Bottazzi), Rend. Lincei Mat. Appl. 26 (2015), pp. 1–11. Intersections of shifted sets, The Electronic Journal of Combinatorics, vol. 22 issue 2 (2015), pp. 7. Intersections of sets of distances, Integers, vol. 16 (2016), A85, pp. 18. A taste of nonstandard methods in combinatorics of numbers, chapter in "Geometry, Structure and Randomness in Combinatorics", CRM Series, Scuola Normale Superiore, Pisa, 2015. Finite embeddability of sets and ultrafilters (with A. Blass), Bulletin Polish Acad. Sci. Math. 63 (2015) , 195-206. High density piecewise syndeticity of sumsets  (with I. Goldbring, R. Jin, S. Leth, M.Lupini, K. Mahlburg), Advances in Mathematics, vol. 278 (2015),  pp. 1-33. On a sumset conjecture by Erdös. (with I. Goldbring, R. Jin, S. Leth, M.Lupini, K. Mahlburg), Canadian Journal of Mathematics, vol. 67 (2015), pp. 795-809.  Iterated hyper-extensions and an idempotent ultrafilter proof of Rado's theorem, Proceedings of the American Mathematical Society, vol. 143 (2015), pp. 1749-1761.  Elementary numerosity and measures. (with V. Benci and E. Bottazzi), Journal of Logic and Analysis, vol. 6 (2014).  Nonstandard analysis and the sumset phenomenon in arbitrary amenable groups (with M. Lupini), Illinois Journal of Mathematics, vol. 58 (2014), pp. 11-25. An elementary proof of Jin's Theorem with a bound, The Electronic Journal of Combinatorics, vol. 21 issue 2 (2014), pp. 7.    Embeddability properties of difference sets, Integers, vol. 14 (2014), A27,  pp. 24. Quasi-selective ultrafilters and asymptotic numerosities  (with A. Blass and M. Forti), Advances in Mathematics, vol. 231 (2012), 1462-86. Fine asymptotic densities for sets of natural numbers , Proceedings of the American Mathematical Society, vol. 138 (2010), pp. 2657-65. Numerosities of point sets over the real line (with M. Forti), Transactions of the American Mathematical Society, vol. 362 (2010), pp. 5355-71. A Euclidean measure of size for mathematical universes (with V. Benci and M. Forti), Logique et Analyse, vol. 197 (2007), pp. 43-52. An Aristotelian notion of size (with V. Benci and M. Forti), Annals of Pure and Applied Logic, vol. 143 (2006), pp. 43-53. The eightfold path to nonstandard analysis (with V. Benci and M. Forti), in "Nonstandard Methods and Applications in Mathematics" (N.J. Cutland, M. Di Nasso and D.A. Ross, eds.), Lecture Notes in Logic vol. 25, ASL, AK Peters, 2006, pp. 3-44. Hausdorff ultrafilters (with M. Forti), Proceedings of the American Mathematical Society, vol. 134 (2006), pp. 1809-1818. Ultrafilter semirings and nonstandard submodels of the Stone-Cech compactification of the natural numbers (with M. Forti), in "Logic and its Applications" (A. Blass and Y. Zhang, eds.), AMS Contemporary Mathematics, vol. 380, 2005, pp. 45-51. Topological and nonstandard extensions (with M. Forti), Monatshefte fur Mathematik, vol. 144 (2005), pp. 89-112. Hausdorff nonstandard extensions (with V. Benci and M. Forti), Bol. Soc. Parana. Mat. (new series), vol. 20 (2002), pp. 9-20. A purely algebraic characterization of the hyperreal numbers (with V. Benci), Proceedings of the American Mathematical Society, vol. 133 (2005), pp. 2501-2505. Alpha-theory: an elementary axiomatics for nonstandard analysis (with V. Benci), Expositiones Mathematicae, vol. 21 (2003), pp. 355-386. Numerosities of labelled sets: a new way of counting (with V. Benci), Advances in Mathematics, vol 173 (2003), pp. 50-67. On the ordering of the nonstandard real line (with M. Forti), in "Logic and Algebra",  AMS Contemporary Mathematics, vol. 302, 2002, pp. 259-273. Nonstandard analysis and an application to the symmetric group on the natural numbers (with Y. Zhang), in "Logic and Algebra", AMS Contemporary Mathematics, vol. 302, 2002, pp. 249-258. Combinatorial principles in nonstandard analysis (with K. Hrbacek), Annals of Pure and Applied Logic, vol.119 (2003), pp. 265-293. A ring homomorphism is enough to get nonstandard analysis (with V. Benci), Bulletin of the Belgian Mathematical Society, vol. 10 (2003), pp. 1-10. Nonstandard analysis by means of ideal values of sequences, in "Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum" (P. Schuster, U. Berger and H. Osswald, eds.), Synthese Library, Kluwer Academic Publishers, vol. 306 (2001), pp. 63-73. On the foundations of nonstandard mathematics, Mathematica Japonica, vol. 50, n.1 (1999), pp. 131-160. The generic filter property in nonstandard analysis, Annals of Pure and Applied Logic, vol. 111 (2001), pp. 23-37. An axiomatic presentation of the nonstandard methods in mathematics, Journal of Symbolic Logic, vol. 67 (2002), pp. 315-325. Pseudo-superstructures as nonstandard universes, Journal of Symbolic Logic, vol.63, n.1 (1998), pp. 222-236. Linearly stratified models for the foundations of nonstandard set theory, Mathematical Logic Quarterly, vol. 44 (1998), pp. 138-142. *ZFC: an axiomatic *approach to nonstandard methods, Comptes Rendus Académie Sciences Paris, t. 324, Serie I, n.9 (1997), pp. 963-967. Hyperordinals and nonstandard alpha-models, in "Logic and Algebra" (A.Ursini and P.Agliano' eds.), Lecture Notes in Pure and Applied Mathematics, vol.180, 1996, Marcel Dekker, New York, pp. 457-475. (In Italiano) Un'introduzione all'analisi con infinitesimi, in "Analisi nonstandard per le scuole superiori - V Giornata di studio" (Atti del convegno, Verona, 10 Ottobre 2015), Matematicamente.it, 2016. (In Italiano) I numeri infinitesimi e l'analisi nonstandard, Archimede, 2003 n.1, pp. 13-22.