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<p>In recent years, several problems regarding the partition regularity of exponential configurations have been studied in the literature, in some cases using the properties of specific ultrafilters. In this paper, we start to lay down the foundations of a general theory of exponentiations of ultrafilters, with a particular focus on their combinatorial properties and the existence of idempotents.</p>

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Exponentiations of ultrafilters

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月19日

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  • Lorenzo Luperi Baglini

摘要

In recent years, several problems regarding the partition regularity of exponential configurations have been studied in the literature, in some cases using the properties of specific ultrafilters. In this paper, we start to lay down the foundations of a general theory of exponentiations of ultrafilters, with a particular focus on their combinatorial properties and the existence of idempotents.