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Nonstandard characterisations of tensor products and monads in the theory of ultrafilters
Author(s) -
Luperi Baglini Lorenzo
Publication year - 2019
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201800089
Subject(s) - mathematics , iterated function , partition (number theory) , tensor (intrinsic definition) , tensor product , pure mathematics , diophantine equation , algebra over a field , combinatorics , mathematical analysis
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.