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RAMSEY’S COHEIRS

Part of: Extremal combinatorics Model theory Nonstandard models

Published online by Cambridge University Press:  15 February 2021

EUGENIO COLLA  and
DOMENICO ZAMBELLA
EUGENIO COLLA
Affiliation:
DIPARTIMENTO DI MATEMATICA UNIVERSITÀ DEGLI STUDI DI TORINOTORINO10100, ITALYE-mail: eugenio.colla@unito.itE-mail: domenico.zambella@unito.it
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Abstract

We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey’s theorem itself. Then we prove Hindman’s theorem and the Hales–Jewett theorem. Finally, we prove two Ramsey theoretic principles that have among their consequences partition theorems due to Carlson and to Gowers.

Keywords

model theoretic methodsRamsey theoryHales-Jewett theorempartition regularity

MSC classification

Primary: 05D10: Ramsey theory
Secondary: 03C98: Applications of model theory 03H99: None of the above, but in this section
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 1 , March 2022 , pp. 377 - 391
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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