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Nonstandard characterisations of tensor products and monads in the theory of ultrafilters
Mathematical Logic Quarterly 65 (3):347-369 (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. Several applications are described by means of multiple examples.My notes
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Citations of this work
Self-Divisible Ultrafilters and Congruences In.Mauro di Nasso, Lorenzo Luperi Baglini, Rosario Mennuni, Moreno Pierobon & Mariaclara Ragosta - forthcoming - Journal of Symbolic Logic:1-18.
References found in this work
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Some applications of iterated ultrapowers in set theory.Kenneth Kunen - 1970 - Annals of Mathematical Logic 1 (2):179.
$$\mathcal {F}$$ F -finite embeddabilities of sets and ultrafilters.Lorenzo Luperi Baglini - 2016 - Archive for Mathematical Logic 55 (5-6):705-734.
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