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.
Nonstandard characterisations of tensor products and monads in the theory of ultrafilters / L. LUPERI BAGLINI. - In: MATHEMATICAL LOGIC QUARTERLY. - ISSN 1521-3870. - (2019 Oct 07). [Epub ahead of print] [10.1002/malq.201800089]
Nonstandard characterisations of tensor products and monads in the theory of ultrafilters
L. LUPERI BAGLINI
2019
Abstract
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.File | Dimensione | Formato | |
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