{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T18:23:36Z","timestamp":1725819816901},"publisher-location":"Pisa","reference-count":20,"publisher":"Scuola Normale Superiore","isbn-type":[{"type":"print","value":"9788876425240"},{"type":"electronic","value":"9788876425257"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-88-7642-525-7_3","type":"book-chapter","created":{"date-parts":[[2015,4,9]],"date-time":"2015-04-09T05:03:54Z","timestamp":1428555834000},"page":"27-46","source":"Crossref","is-referenced-by-count":1,"title":["A taste of nonstandard methods in combinatorics of numbers"],"prefix":"10.1007","author":[{"given":"Mauro","family":"Di Nasso","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"L.O. Arkeryd, N.J. Cutland and C.W. Henson, eds., \u201cNonstandard Analysis \u2014 Theory and Applications\u201d, NATO ASI Series C, Vol. 493, Kluwer A.P., 1997.","DOI":"10.1007\/978-94-011-5544-1"},{"key":"3_CR2","doi-asserted-by":"crossref","first-page":"481","DOI":"10.36045\/bbms\/1070645796","volume":"10","author":"V Benci","year":"2003","unstructured":"V. Benci and M. Di Nasso, A ring homomorphism is enough to get nonstandard analysis, Bull. Belg. Math. Soc. 10 (2003), 481\u2013490.","journal-title":"Bull. Belg. Math. Soc."},{"key":"3_CR3","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1090\/S0002-9947-1990-0982232-5","volume":"320","author":"V Bergelson","year":"1990","unstructured":"V. Bergelson and N. Hindman, Non-metrizable topological dynamics and Ramsey theory, Trans. Am. Math. Soc. 320 (1990), 293\u2013320.","journal-title":"Trans. Am. Math. Soc."},{"key":"3_CR4","unstructured":"C.C. Chang and H.J. Keisler, \u201cModel Theory\u201d (3rd edition), North-Holland, 1990."},{"key":"3_CR5","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s00493-012-2697-9","volume":"32","author":"P Csikvari","year":"2012","unstructured":"P. Csikvari, K. Gyarmati and A. Sarkozy, Density and Ramsey type results on algebraic equations with restricted solution sets, Combinatorica 32 (2012), 425\u2013449.","journal-title":"Combinatorica"},{"key":"3_CR6","first-page":"A27","volume":"14","author":"M Nasso Di","year":"2014","unstructured":"M. Di Nasso, Embeddability properties of difference sets, Integers 14 (2014), A27.","journal-title":"Integers"},{"key":"3_CR7","unstructured":"M. Di Nasso, Iterated hyper-extensions and an idempotent ultrafilter proof of Rado\u2019s theorem, Proc. Amer. Math. Soc., to appear."},{"key":"3_CR8","unstructured":"M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini and K. Mahlburg, Progress on a sumset conjecture by Erd\u00f6s, Arxiv:1307.0767, 2013."},{"key":"3_CR9","unstructured":"M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini and K. Mahlburg, High density piecewise syndeticity of sumsets, Arxiv:1310.5729, 2013."},{"key":"3_CR10","doi-asserted-by":"crossref","unstructured":"R. Goldblatt, \u201cLectures on the Hyperreals \u2014 An Introduction to Nonstandard Analysis\u201d, Graduate Texts in Mathematics, Vol. 188, Springer, 1998.","DOI":"10.1007\/978-1-4612-0615-6"},{"key":"3_CR11","doi-asserted-by":"crossref","unstructured":"N. Hindman and D. Strauss, \u201cAlgebra in the Stone-\u010cech Compactification\u201d (2nd edition), Walter de Gruyter, 2012.","DOI":"10.1515\/9783110258356"},{"key":"3_CR12","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1006\/jnth.2001.2671","volume":"91","author":"R Jin","year":"2001","unstructured":"R. Jin, Nonstandard methods for upper Banach density problems, J. Number Theory 91 (2001), 20\u201338.","journal-title":"J. Number Theory"},{"key":"3_CR13","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1090\/S0002-9939-01-06088-9","volume":"130","author":"R Jin","year":"2002","unstructured":"R. Jin, The sumset phenomenon, Proc. Amer. Math. Soc. 130 (2002), 855\u2013861.","journal-title":"Proc. Amer. Math. Soc."},{"key":"3_CR14","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/j.aim.2007.06.002","volume":"216","author":"R Jin","year":"2007","unstructured":"R. Jin, Freimans inverse problem with small doubling property, Adv. Math. 216 (2007), 711\u2013752.","journal-title":"Adv. Math."},{"issue":"2","key":"3_CR15","first-page":"A7","volume":"8","author":"R Jin","year":"2008","unstructured":"R. Jin, Introduction of nonstandard methods for number theorists, Proceedings of the CANT (2005) \u2014 Conference in Honor of Mel Nathanson, Integers 8 (2) (2008), A7.","journal-title":"Integers"},{"key":"3_CR16","doi-asserted-by":"publisher","first-page":"1785","DOI":"10.1016\/j.jnt.2010.02.008","volume":"130","author":"R Jin","year":"2010","unstructured":"R. Jin, Characterizing the structure of A+B when A+B has small upper Banach density, J. Number Theory 130 (2010), 1785\u20131800.","journal-title":"J. Number Theory"},{"key":"3_CR17","doi-asserted-by":"publisher","first-page":"5059","DOI":"10.1090\/S0002-9947-2011-05533-9","volume":"363","author":"R Jin","year":"2011","unstructured":"R. Jin, Plunnecke\u2019s theorem for asymptotic densities, Trans. Amer. Math. Soc. 363 (2011), 5059\u20135070.","journal-title":"Trans. Amer. Math. Soc."},{"key":"3_CR18","volume-title":"Elementary Calculus \u2014 An Infinitesimal Approach","author":"H J Keisler","year":"1986","unstructured":"H.J. Keisler, \u201cElementary Calculus \u2014 An Infinitesimal Approach\u201d (2nd edition), Prindle, Weber & Schmidt, Boston, 1986. (This book is now freely downloadable from the author\u2019s homepage: http:\/\/www.math.wisc.edu\/\u223ckeisler\/calc.html.)","edition":"2nd"},{"key":"3_CR19","first-page":"A30","volume":"14","author":"L Luperi Baglini","year":"2014","unstructured":"L. Luperi Baglini, Partition regularity of nonlinear polynomials: a nonstandard approach, Integers 14 (2014), A30.","journal-title":"Integers"},{"key":"3_CR20","first-page":"319","volume":"13","author":"I Z Ruzsa","year":"1978","unstructured":"I.Z. Ruzsa, On difference sets, Studia Sci. Math. Hungar. 13 (1978), 319\u2013326.","journal-title":"Studia Sci. Math. Hungar."}],"container-title":["Geometry, Structure and Randomness in Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-88-7642-525-7_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T17:15:31Z","timestamp":1598894131000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-88-7642-525-7_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9788876425240","9788876425257"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-88-7642-525-7_3","relation":{},"subject":[],"published":{"date-parts":[[2014]]}}}