In [F81] Furstenberg introduced the notion of central set and established his famous Central Sets Theorem. Since then, several improved versions of Furstenberg's result have been found. The strongest generalization has been published by De, Hindman and Strauss in [DHS08], whilst a polynomial extension by Bergelson, Johnson and Moreira appeared in [BJM17]. In this article, we will establish a polynomial extension of the stronger version of the central sets theorem, and we will discuss properties of the families of sets that this result leads to consider.

Polynomial extension of the Stronger Central Sets Theorem / S. Goswami, L. LUPERI BAGLINI, S. Kanti Patra. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - 30:4(2023 Dec 01), pp. P4.36.1-P4.36.13. [10.37236/11556]

Polynomial extension of the Stronger Central Sets Theorem

L. LUPERI BAGLINI
Penultimo
;
2023

Abstract

In [F81] Furstenberg introduced the notion of central set and established his famous Central Sets Theorem. Since then, several improved versions of Furstenberg's result have been found. The strongest generalization has been published by De, Hindman and Strauss in [DHS08], whilst a polynomial extension by Bergelson, Johnson and Moreira appeared in [BJM17]. In this article, we will establish a polynomial extension of the stronger version of the central sets theorem, and we will discuss properties of the families of sets that this result leads to consider.
central sets; ultrafilters; nonstandard analysis;
Settore MAT/01 - Logica Matematica
   Logical methods in combinatorics
   MINISTERO DELL'UNIVERSITA' E DELLA RICERCA
   2022BXH4R5_001
1-dic-2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/938909
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