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Nonstandard characterisations of tensor products and monads in the theory of ultrafilters
Mathematical Logic Quarterly ( IF 0.3 ) Pub Date : 2019-10-01 , DOI: 10.1002/malq.201800089
Lorenzo Luperi Baglini 1
Affiliation  

We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as by characterising their combinatorial properties by means of their monads. This extends to arbitrary sets and properties methods previously used to study partition regular Diophantine equations on N. Several applications are described by means of multiple examples.

中文翻译:

超滤器理论中张量积和单子的非标准特征

我们使用基于迭代超扩展的非标准方法来开发对超滤器单子理论的拉姆齐理论的应用。这是通过详细研究超滤器的任意张量积,以及通过它们的单子来表征它们的组合特性来实现的。这扩展到以前用于研究 N 上的分区正则丢番图方程的任意集合和属性方法。通过多个示例描述了几个应用程序。
更新日期:2019-10-01
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