Di Nasso, Mauro; Ragosta, Mariaclara Monochromatic exponential triples: an ultrafilter proof. (English) Zbl 1525.05187 Proc. Am. Math. Soc. 152, No. 1, 81-87 (2024). MSC: 05D10 05A17 54D80 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Ragosta}, Proc. Am. Math. Soc. 152, No. 1, 81--87 (2024; Zbl 1525.05187) Full Text: DOI arXiv
Di Nasso, Mauro; Baglini, Lorenzo Luperi; Mennuni, Rosario; Pierobon, Moreno; Ragosta, Mariaclara Self-divisible ultrafilters and congruences in \(\beta\mathbb{Z}\). arXiv:2302.09983 Preprint, arXiv:2302.09983 [math.LO] (2023). MSC: 54D80 11A07 03H15 03C62 20E18 BibTeX Cite \textit{M. Di Nasso} et al., ``Self-divisible ultrafilters and congruences in $\beta\mathbb{Z}$'', Preprint, arXiv:2302.09983 [math.LO] (2023) Full Text: DOI arXiv OA License
Di Nasso, Mauro; Ragosta, Mariaclara Central sets and infinite monochromatic exponential patterns. arXiv:2211.16269 Preprint, arXiv:2211.16269 [math.CO] (2022). MSC: 05D10 05A17 54D80 BibTeX Cite \textit{M. Di Nasso} and \textit{M. Ragosta}, ``Central sets and infinite monochromatic exponential patterns'', Preprint, arXiv:2211.16269 [math.CO] (2022) Full Text: arXiv OA License
Di Nasso, Mauro; Goldbring, Isaac; Lupini, Martino Nonstandard methods in Ramsey theory and combinatorial number theory. (English) Zbl 1432.05001 Lecture Notes in Mathematics 2239. Cham: Springer (ISBN 978-3-030-17955-7/pbk; 978-3-030-17956-4/ebook). xvi, 204 p. (2019). Reviewer: M. P. Chaudhary (New Delhi) MSC: 05-02 05D10 05C55 11B75 26E35 00-01 00-02 03H05 28E05 30G06 46S20 47S20 54J05 PDFBibTeX XMLCite \textit{M. Di Nasso} et al., Nonstandard methods in Ramsey theory and combinatorial number theory. Cham: Springer (2019; Zbl 1432.05001) Full Text: DOI arXiv Link
Benci, Vieri; Di Nasso, Mauro How to measure the infinite. Mathematics with infinite and infinitesimal numbers. (English) Zbl 1429.26001 Hackensack, NJ: World Scientific (ISBN 978-981-283-637-3/hbk; 978-981-327-660-4/ebook). xxviii, 317 p. (2019). Reviewer: Miroslav Repický (Košice) MSC: 26-02 26E35 28E05 46F05 54J05 60E05 03E35 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Di Nasso}, How to measure the infinite. Mathematics with infinite and infinitesimal numbers. Hackensack, NJ: World Scientific (2019; Zbl 1429.26001) Full Text: DOI
Di Nasso, Mauro; Baglini, Lorenzo Luperi Ramsey properties of nonlinear Diophantine equations. (English) Zbl 1376.05159 Adv. Math. 324, 84-117 (2018). MSC: 05D10 11D99 11B30 03H05 11U10 54D80 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{L. L. Baglini}, Adv. Math. 324, 84--117 (2018; Zbl 1376.05159) Full Text: DOI arXiv
Di Nasso, Mauro; Tachtsis, Eleftherios Idempotent ultrafilters without Zorn’s lemma. (English) Zbl 1427.03053 Proc. Am. Math. Soc. 146, No. 1, 397-411 (2018). MSC: 03E25 03E05 54D80 05D10 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{E. Tachtsis}, Proc. Am. Math. Soc. 146, No. 1, 397--411 (2018; Zbl 1427.03053) Full Text: DOI arXiv
Blass, Andreas; Di Nasso, Mauro Finite embeddability of sets and ultrafilters. (English) Zbl 1382.03068 Bull. Pol. Acad. Sci., Math. 63, No. 3, 195-206 (2015). MSC: 03E05 03H15 03C20 54D80 PDFBibTeX XMLCite \textit{A. Blass} and \textit{M. Di Nasso}, Bull. Pol. Acad. Sci., Math. 63, No. 3, 195--206 (2015; Zbl 1382.03068) Full Text: DOI arXiv
Di Nasso, Mauro Hypernatural Numbers as Ultrafilters. arXiv:1501.05755 Preprint, arXiv:1501.05755 [math.LO] (2015). MSC: 03H05 03E05 54D80 BibTeX Cite \textit{M. Di Nasso}, ``Hypernatural Numbers as Ultrafilters'', Preprint, arXiv:1501.05755 [math.LO] (2015) Full Text: arXiv OA License
Benci, Vieri; Forti, Marco; Di Nasso, Mauro The eightfold path to nonstandard analysis. (English) Zbl 1104.03061 Cutland, Nigel J. (ed.) et al., Nonstandard methods and applications in mathematics. Wellesley, MA: A K Peters; Urbana, IL: Association for Symbolic Logic (ASL) (ISBN 1-56881-291-4/hbk; 1-56881-292-2/pbk). Lecture Notes in Logic 25, 3-44 (2006). Reviewer: German Pestov (Tomsk) MSC: 03H05 26E35 03E65 54J05 PDFBibTeX XMLCite \textit{V. Benci} et al., Lect. Notes Log. 25, 3--44 (2006; Zbl 1104.03061)
Di Nasso, Mauro; Forti, Marco Hausdorff ultrafilters. (English) Zbl 1096.03056 Proc. Am. Math. Soc. 134, No. 6, 1809-1818 (2006). Reviewer: Kiyoshi Iseki (Osaka) MSC: 03E05 03H05 54D80 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Forti}, Proc. Am. Math. Soc. 134, No. 6, 1809--1818 (2006; Zbl 1096.03056) Full Text: DOI
Di Nasso, Mauro; Forti, Marco Ultrafilter semirings and nonstandard submodels of the Stone-Čech compactification of the natural numbers. (English) Zbl 1079.16036 Blass, Andreas (ed.) et al., Logic and its applications. Result of the conference on logic and its applications in algebra and geometry, Ann Arbor, MI, USA, April 11–13, 2003 and the workshop on combinatorial set theory, excellent classes, and Schanuel conjecture, Ann Arbor, MI, USA, April 14–15, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3474-6/pbk). Contemporary Mathematics 380, 45-51 (2005). MSC: 16Y60 03H15 54D80 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Forti}, Contemp. Math. 380, 45--51 (2005; Zbl 1079.16036)
Benci, Vieri; Di Nasso, Mauro A purely algebraic characterization of the hyperreal numbers. (English) Zbl 1113.26028 Proc. Am. Math. Soc. 133, No. 9, 2501-2505 (2005). MSC: 26E35 16S60 54C40 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Di Nasso}, Proc. Am. Math. Soc. 133, No. 9, 2501--2505 (2005; Zbl 1113.26028) Full Text: DOI
Di Nasso, Mauro; Forti, Marco Topological and nonstandard extensions. (English) Zbl 1073.54015 Monatsh. Math. 144, No. 2, 89-112 (2005). Reviewer: Paul Bankston (Milwaukee) MSC: 54D35 03H05 03C20 54J05 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Forti}, Monatsh. Math. 144, No. 2, 89--112 (2005; Zbl 1073.54015) Full Text: DOI
Forti, Marco; Di Nasso, Mauro; Benci, Vieri Hausdorff nonstandard extensions. (English) Zbl 1061.54018 Bol. Soc. Parana. Mat. (3) 20, No. 1-2, 9-20 (2002). Reviewer: T. Thrivikraman (Cochin) MSC: 54D35 03H05 03C20 54D80 54J05 PDFBibTeX XMLCite \textit{M. Forti} et al., Bol. Soc. Parana. Mat. (3) 20, No. 1--2, 9--20 (2002; Zbl 1061.54018)