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. - (2022 Sep 21).

Polynomial extension of the Stronger Central Sets Theorem

L. LUPERI BAGLINI
;
2022

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
https://arxiv.org/abs/2209.10253
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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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