Partition regularity and multiplicatively syndetic sets
نویسندگان
چکیده
منابع مشابه
Universally Image Partition Regularity
Many of the classical results of Ramsey Theory, for example Schur’s Theorem, van der Waerden’s Theorem, Finite Sums Theorem, are naturally stated in terms of image partition regularity of matrices. Many characterizations are known of image partition regularity over N and other subsemigroups of (R,+). In this paper we introduce a new notion which we call universally image partition regular matri...
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This is a survey of results on partition regularity of matrices, beginning with the classic results of Richard Rado on kernel partition regularity, continuing with the groundbreaking results of Walter Deuber on image partition regularity, and leading up to the present day. Included are the largely settled world of finite matrices and the mostly unknown world of infinite matrices.
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We define and undertake a systematic study of thick, syndetic, and piecewise syndetic subsets of a Fräıssé structure. Each of these collections forms a family in the sense of Akin and Glasner [AG], and we define and study ultrafilters on each of these families, paying special attention to ultrafilters on the thick sets. In the process, we generalize many results of Bergelson, Hindman, and McCut...
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Many of the classical results of Ramsey Theory are naturally stated in terms of image partition regularity of matrices. Many characterizations are known of image partition regularity over N and other subsemigroups of (R,+). We study several notions of image partition regularity near zero for both finite and infinite matrices, and establish relationships which must hold among these notions.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2020
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa190421-11-3