Over the last years, my research focused on combinatorial number theory; especially in the use of nonstandard methods and ultrafilters in density depending results and in the Ramsey theory of Diophantine equations. I am also interested in foundational theories of counting (numerosities).

I am an associated professor at the Math Department of the University of Pisa. My research field is mathematical logic and its applications, and I am particularly interested in nonstandard analysis and its applications.

2003年1月1日 · 376 V. Benci and M. Di Nasso assumption of an ultrapower where every infinitesimal is originated by some infinitesimal sequence, requires a P-point, an ultrafilter with additional properties whose existence is independent of ZFC. The similar foundational issues arise in our context.

The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting.

2017年9月12日 · View a PDF of the paper titled Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory, by Mauro Di Nasso and 1 other authors

2012年11月18日 · View a PDF of the paper titled Nonstandard Analysis and the sumset phenomenon in arbitrary amenable groups, by Mauro Di Nasso and Martino Lupini

2024年6月8日 · We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard technique for applications in combinatorial number theory. Bibliographic Explorer (What is the Explorer?)

Mauro Di Nasso's 78 research works with 679 citations and 3,581 reads, including: SELF-DIVISIBLE ULTRAFILTERS AND CONGRUENCES IN

Mauro Di Nasso > HOME > CV > PAPERS > DIDATTICA > TESI ... ELEMENTI DI TEORIA DEGLI INSIEMI 2023-2024 GEOMETRIA per Ingegneria Edile-Architettura 2023-2024 ULTRAFILTRI E METODI NONSTANDARD 2023-2024 LOGICA MATEMATICA 2022-2023 GEOMETRIA per Ingegneria Edile-Architettura 2022-2023 ...

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.