Exact big Ramsey degrees for finitely constrained binary free amalgamation classes

Martin Balko; David Chodounský; Natasha Dobrinen; Jan Hubička; Matěj Konečný; Lluís Vena; Andy Zucker

doi:10.4171/jems/1507

Exact big Ramsey degrees for finitely constrained binary free amalgamation classes

Martin Balko
, David Chodounský
, Natasha Dobrinen
, Jan Hubička
, Matěj Konečný
, Lluís Vena
, Andy Zucker

Research output: Contribution to journal › Article › peer-review

Abstract

We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fraïssé limit of each such class admits a big Ramsey structure satisfying the infinite Ramsey theorem, implying that the automorphism group of the Fraïssé limit has a metrizable universal completion flow.

Original language	English
Pages (from-to)	2101-2150
Number of pages	50
Journal	Journal of the European Mathematical Society
Volume	28
Issue number	5
DOIs	https://doi.org/10.4171/jems/1507
State	Published - 1 Jan 2026
Externally published	Yes

Keywords

Fraïssé structures
big Ramsey degrees
binary free amalgamation classes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/jems/1507

Cite this

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title = "Exact big Ramsey degrees for finitely constrained binary free amalgamation classes",

abstract = "We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fra{\"i}ss{\'e} limit of each such class admits a big Ramsey structure satisfying the infinite Ramsey theorem, implying that the automorphism group of the Fra{\"i}ss{\'e} limit has a metrizable universal completion flow.",

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AU - Balko, Martin

AU - Chodounský, David

AU - Dobrinen, Natasha

AU - Hubička, Jan

AU - Konečný, Matěj

AU - Vena, Lluís

AU - Zucker, Andy

PY - 2026/1/1

Y1 - 2026/1/1

N2 - We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fraïssé limit of each such class admits a big Ramsey structure satisfying the infinite Ramsey theorem, implying that the automorphism group of the Fraïssé limit has a metrizable universal completion flow.

AB - We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fraïssé limit of each such class admits a big Ramsey structure satisfying the infinite Ramsey theorem, implying that the automorphism group of the Fraïssé limit has a metrizable universal completion flow.

KW - Fraïssé structures

KW - big Ramsey degrees

KW - binary free amalgamation classes

UR - https://www.scopus.com/pages/publications/105033483250

U2 - 10.4171/jems/1507

DO - 10.4171/jems/1507

M3 - Article

AN - SCOPUS:105033483250

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VL - 28

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JO - Journal of the European Mathematical Society

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IS - 5

ER -

Exact big Ramsey degrees for finitely constrained binary free amalgamation classes

Abstract

Keywords

ASJC Scopus subject areas

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