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; Forti, Marco Euclidean integers, Euclidean ultrafilters, and Euclidean numerosities. arXiv:2207.07505 Preprint, arXiv:2207.07505 [math.LO] (2022). MSC: 03E02 03E65 03H15 BibTeX Cite \textit{M. Di Nasso} and \textit{M. Forti}, ``Euclidean integers, Euclidean ultrafilters, and Euclidean numerosities'', Preprint, arXiv:2207.07505 [math.LO] (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; Jin, Renling Abstract densities and ideals of sets. (English) Zbl 1423.11027 Acta Arith. 185, No. 4, 301-313 (2018). MSC: 11B05 03E05 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{R. Jin}, Acta Arith. 185, No. 4, 301--313 (2018; Zbl 1423.11027) Full Text: DOI arXiv
Di Nasso, Mauro; Riggio, Maria Fermat-like equations that are not partition regular. (English) Zbl 1438.11075 Combinatorica 38, No. 5, 1067-1078 (2018). Reviewer: Stelian Mihalas (Timişoara) MSC: 11D04 03H05 05D10 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Riggio}, Combinatorica 38, No. 5, 1067--1078 (2018; Zbl 1438.11075) Full Text: DOI arXiv
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
Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl High density piecewise syndeticity of product sets in amenable groups. (English) Zbl 1419.11017 J. Symb. Log. 81, No. 4, 1555-1562 (2016). MSC: 11B13 11B05 03H05 43A07 PDFBibTeX XMLCite \textit{M. Di Nasso} et al., J. Symb. Log. 81, No. 4, 1555--1562 (2016; Zbl 1419.11017) Full Text: DOI arXiv Link
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 A taste of nonstandard methods in combinatorics of numbers. (English) Zbl 1391.05052 Matoušek, Jiří (ed.) et al., Geometry, structure and randomness in combinatorics. Lectures of the workshop, Pisa, Italy, September 3–7, 2012. Pisa: Edizioni della Normale (ISBN 978-88-7642-524-0/pbk; 978-88-7642-525-7/ebook). Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series 18, 27-46 (2015). Reviewer: Isaac Goldbring (Irvine) MSC: 05A99 03H05 11B05 11U10 PDFBibTeX XMLCite \textit{M. Di Nasso}, CRM Ser. 18, 27--46 (2015; Zbl 1391.05052) Full Text: DOI arXiv
Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl High density piecewise syndeticity of sumsets. (English) Zbl 1398.11029 Adv. Math. 278, 1-33 (2015). MSC: 11B13 11B05 03H05 03H15 PDFBibTeX XMLCite \textit{M. Di Nasso} et al., Adv. Math. 278, 1--33 (2015; Zbl 1398.11029) Full Text: DOI arXiv
Di Nasso, Mauro Iterated hyper-extensions and an idempotent ultrafilter proof of Rado’s theorem. (English) Zbl 1386.03057 Proc. Am. Math. Soc. 143, No. 4, 1749-1761 (2015). MSC: 03E05 03H05 05D10 11D04 PDFBibTeX XMLCite \textit{M. Di Nasso}, Proc. Am. Math. Soc. 143, No. 4, 1749--1761 (2015; Zbl 1386.03057) 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
Di Nasso, Mauro; Lupini, Martino Nonstandard analysis and the sumset phenomenon in arbitrary amenable groups. (English) Zbl 1320.03092 Ill. J. Math. 58, No. 1, 11-25 (2014). MSC: 03H05 43A07 11B05 11B13 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Lupini}, Ill. J. Math. 58, No. 1, 11--25 (2014; Zbl 1320.03092) Full Text: arXiv Euclid
Di Nasso, Mauro Embeddability properties of difference sets. (English) Zbl 1353.03084 Integers 14, Paper A27, 24 p. (2014). MSC: 03H05 11B05 11B13 PDFBibTeX XMLCite \textit{M. Di Nasso}, Integers 14, Paper A27, 24 p. (2014; Zbl 1353.03084) Full Text: arXiv EMIS
Blass, Andreas; Di Nasso, Mauro; Forti, Marco Quasi-selective ultrafilters and asymptotic numerosities. (English) Zbl 1270.03105 Adv. Math. 231, No. 3-4, 1462-1486 (2012). MSC: 03E65 03E05 03C20 PDFBibTeX XMLCite \textit{A. Blass} et al., Adv. Math. 231, No. 3--4, 1462--1486 (2012; Zbl 1270.03105) Full Text: DOI arXiv
Bergelson, Vitaly (ed.); Blass, Andreas (ed.); Di Nasso, Mauro (ed.); Jin, Renling (ed.) Ultrafilters across mathematics. International congress ULTRAMATH 2008: Applications of ultrafilters and ultraproducts in mathematics, Pisa, Italy, June 1–7, 2008. (English) Zbl 1202.03009 Contemporary Mathematics 530. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4833-3/pbk). ix, 200 p. (2010). MSC: 03-06 03C20 03E05 03H05 05C55 28E15 00B25 PDFBibTeX XMLCite \textit{V. Bergelson} (ed.) et al., Ultrafilters across mathematics. International congress ULTRAMATH 2008: Applications of ultrafilters and ultraproducts in mathematics, Pisa, Italy, June 1--7, 2008. Providence, RI: American Mathematical Society (AMS) (2010; Zbl 1202.03009) Full Text: DOI
Di Nasso, Mauro; Forti, Marco Numerosities of point sets over the real line. (English) Zbl 1200.03033 Trans. Am. Math. Soc. 362, No. 10, 5355-5371 (2010). MSC: 03E10 03C20 03E05 03H05 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Forti}, Trans. Am. Math. Soc. 362, No. 10, 5355--5371 (2010; Zbl 1200.03033) Full Text: DOI
Di Nasso, Mauro Fine asymptotic densities for sets of natural numbers. (English) Zbl 1247.11014 Proc. Am. Math. Soc. 138, No. 8, 2657-2665 (2010). MSC: 11B05 03E35 PDFBibTeX XMLCite \textit{M. Di Nasso}, Proc. Am. Math. Soc. 138, No. 8, 2657--2665 (2010; Zbl 1247.11014) Full Text: DOI
Benci, Vieri; Di Nasso, Mauro; Forti, Marco An Euclidean measure of size for mathematical universes. (English) Zbl 1131.03029 Log. Anal., Nouv. Sér. 50, No. 197, 43-62 (2007). Reviewer: Nicolae A. Soare (Bucureşti) MSC: 03E99 03B30 PDFBibTeX XMLCite \textit{V. Benci} et al., Log. Anal., Nouv. Sér. 50, No. 197, 43--62 (2007; Zbl 1131.03029)
Benci, Vieri; Di Nasso, Mauro; Forti, Marco An Aristotelian notion of size. (English) Zbl 1114.03055 Ann. Pure Appl. Logic 143, No. 1-3, 43-53 (2006). Reviewer: Roman Kossak (New York) MSC: 03H05 03E70 PDFBibTeX XMLCite \textit{V. Benci} et al., Ann. Pure Appl. Logic 143, No. 1--3, 43--53 (2006; Zbl 1114.03055) Full Text: DOI
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)
Cutland, Nigel J. (ed.); Di Nasso, Mauro (ed.); Ross, David A. (ed.) Nonstandard methods and applications in mathematics. (English) Zbl 1083.03005 Lecture Notes in Logic 25. Wellesley, MA: A K Peters; Urbana, IL: Association for Symbolic Logic (ASL) (ISBN 1-56881-291-4/hbk; 1-56881-292-2/pbk). ix, 248 p. (2006). MSC: 03-06 03H05 00B25 PDFBibTeX XMLCite \textit{N. J. Cutland} (ed.) et al., Nonstandard methods and applications in mathematics. Wellesley, MA: A K Peters; Urbana, IL: Association for Symbolic Logic (ASL) (2006; Zbl 1083.03005)
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)
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
Benci, Vieri; Di Nasso, Mauro A ring homomorphism is enough to get nonstandard analysis. (English) Zbl 1062.03066 Bull. Belg. Math. Soc. - Simon Stevin 10, No. 4, 481-490 (2003). Reviewer: Mihail I. Ursul (Oradea) MSC: 03H05 26E35 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Di Nasso}, Bull. Belg. Math. Soc. - Simon Stevin 10, No. 4, 481--490 (2003; Zbl 1062.03066)
Benci, Vieri; Di Nasso, Mauro Alpha-theory: An elementary axiomatics for nonstandard analysis. (English) Zbl 1038.26019 Expo. Math. 21, No. 4, 355-386 (2003). Reviewer: W. A. J. Luxemburg (Pasadena) MSC: 26E35 03H05 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Di Nasso}, Expo. Math. 21, No. 4, 355--386 (2003; Zbl 1038.26019) Full Text: DOI
Benci, Vieri; Di Nasso, Mauro Numerosities of labelled sets: A new way of counting. (English) Zbl 1028.03042 Adv. Math. 173, No. 1, 50-67 (2003). Reviewer: K.Iséki (Osaka) MSC: 03E65 03C20 03E35 03H05 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Di Nasso}, Adv. Math. 173, No. 1, 50--67 (2003; Zbl 1028.03042) Full Text: DOI
Di Nasso, Mauro; Hrbacek, Karel Combinatorial principles in nonstandard analysis. (English) Zbl 1016.03070 Ann. Pure Appl. Logic 119, No. 1-3, 265-293 (2003). Reviewer: Robert A.Herrmann (Annapolis) MSC: 03H05 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{K. Hrbacek}, Ann. Pure Appl. Logic 119, No. 1--3, 265--293 (2003; Zbl 1016.03070) 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)
Di Nasso, Mauro; Forti, Marco On the ordering of the nonstandard real line. (English) Zbl 1016.03071 Zhang, Yi (ed.), Logic and algebra. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 302, 259-273 (2002). Reviewer: Robert A.Herrmann (Annapolis) MSC: 03H05 03C20 06F30 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Forti}, Contemp. Math. 302, 259--273 (2002; Zbl 1016.03071)
Di Nasso, Mauro; Zhang, Yi Nonstandard analysis and an application to the symmetric group on natural numbers. (English) Zbl 1020.03064 Zhang, Yi (ed.), Logic and algebra. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 302, 249-258 (2002). MSC: 03H05 20B30 PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{Y. Zhang}, Contemp. Math. 302, 249--258 (2002; Zbl 1020.03064)
Di Nasso, Mauro An axiomatic presentation of the nonstandard methods in mathematics. (English) Zbl 1005.03053 J. Symb. Log. 67, No. 1, 315-325 (2002). Reviewer: Yuri Movsisyan (Yerevan) MSC: 03H05 03E70 PDFBibTeX XMLCite \textit{M. Di Nasso}, J. Symb. Log. 67, No. 1, 315--325 (2002; Zbl 1005.03053) Full Text: DOI Link
Di Nasso, Mauro Nonstandard analysis by means of ideal values of sequences. (English) Zbl 1010.03057 Schuster, Peter (ed.) et al., Reuniting the antipodes–constructive and nonstandard views of the continuum. Symposium proceedings, San Servolo, Venice, Italy, May 16-22, 1999. Dordrecht: Kluwer Academic Publishers. Synth. Libr. 306, 63-73 (2001). MSC: 03H05 26E35 03E70 03C20 03E35 PDFBibTeX XMLCite \textit{M. Di Nasso}, Synth. Libr. 306, 63--73 (2001; Zbl 1010.03057)
Di Nasso, Mauro The generic filter property in nonstandard analysis. (English) Zbl 0981.03069 Ann. Pure Appl. Logic 111, No. 1-2, 23-37 (2001). Reviewer: Robert A.Herrmann (Annapolis) MSC: 03H05 03C52 03E05 PDFBibTeX XMLCite \textit{M. Di Nasso}, Ann. Pure Appl. Logic 111, No. 1--2, 23--37 (2001; Zbl 0981.03069) Full Text: DOI
Di Nasso, Mauro On the foundations of nonstandard mathematics. (English) Zbl 0937.03075 Math. Jap. 50, No. 1, 131-160 (1999). Reviewer: R.A.Herrmann (Annapolis) MSC: 03Hxx 03E70 PDFBibTeX XMLCite \textit{M. Di Nasso}, Math. Japon. 50, No. 1, 131--160 (1999; Zbl 0937.03075)
Di Nasso, Mauro Pseudo-superstructures as nonstandard universes. (English) Zbl 0902.03040 J. Symb. Log. 63, No. 1, 222-236 (1998). Reviewer: R.A.Herrmann (Annapolis) MSC: 03H99 03E30 PDFBibTeX XMLCite \textit{M. Di Nasso}, J. Symb. Log. 63, No. 1, 222--236 (1998; Zbl 0902.03040) Full Text: DOI Link
Di Nasso, Mauro Linearly stratified models for the foundations of nonstandard mathematics. (English) Zbl 0891.03035 Math. Log. Q. 44, No. 1, 138-142 (1998). Reviewer: W.A.J.Luxemburg (Pasadena) MSC: 03H99 03C20 03C62 03E55 PDFBibTeX XMLCite \textit{M. Di Nasso}, Math. Log. Q. 44, No. 1, 138--142 (1998; Zbl 0891.03035) Full Text: DOI
Di Nasso, Mauro *ZFC: An axiomatic *approach to nonstandard methods. (English. Abridged French version) Zbl 0906.03066 C. R. Acad. Sci., Paris, Sér. I 324, No. 9, 963-967 (1997); erratum ibid. 325, 5 (1997). Reviewer: K.Iséki (Osaka) MSC: 03H05 03E70 PDFBibTeX XMLCite \textit{M. Di Nasso}, C. R. Acad. Sci., Paris, Sér. I 324, No. 9, 963--967 (1997); erratum ibid. 325, 5 (1997; Zbl 0906.03066) Full Text: DOI
Di Nasso, Mauro Hyperordinals and nonstandard \(\alpha\)-models. (English) Zbl 0855.03041 Ursini, Aldo (ed.) et al., Logic and algebra. Proceedings of the international conference dedicated to the memory of Roberto Magari, April 26–30, 1994, Pontignano, Italy. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 180, 457-475 (1996). MSC: 03H05 03E70 PDFBibTeX XMLCite \textit{M. Di Nasso}, Lect. Notes Pure Appl. Math. 180, 457--475 (1996; Zbl 0855.03041)