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Exact big Ramsey degrees for finitely constrained binary free amalgamation classes

  • Martin Balko

    Charles University, Praha 1, Czech Republic

  • David Chodounský

    Charles University, Praha 1, Czech Republic; Czech Academy of Sciences, Praha 1, Czech Republic

  • Natasha Dobrinen

    University of Notre Dame, Notre Dame, USA

  • Jan Hubička

    Charles University, Praha 1, Czech Republic

  • Matěj Konečný

    TU Dresden, Dresden, Germany; Charles University, Praha 1, Czech Republic

  • Lluís Vena

    Universitat Politècnica de Catalunya, Barcelona, Spain

  • Andy Zucker

    University of Waterloo, Waterloo, Canada
Exact big Ramsey degrees for finitely constrained binary free amalgamation classes cover

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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.

Cite this article

Martin Balko, David Chodounský, Natasha Dobrinen, Jan Hubička, Matěj Konečný, Lluís Vena, Andy Zucker, Exact big Ramsey degrees for finitely constrained binary free amalgamation classes. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1507