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.
Exponentiations of ultrafilters / L. Luperi Baglini. - In: SEMIGROUP FORUM. - ISSN 0037-1912. - 110:3(2025 Jun), pp. 640-654. [10.1007/s00233-025-10530-5]
Exponentiations of ultrafilters
L. Luperi Baglini
2025
Abstract
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.
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