Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T00:51:17.327Z Has data issue: false hasContentIssue false
  • English
  • Français

CORES OVER RAMSEY STRUCTURES

Part of: Graph theory Model theory

Published online by Cambridge University Press:  01 February 2021

ANTOINE MOTTET  and
MICHAEL PINSKER
ANTOINE MOTTET
Affiliation:
DEPARTMENT OF ALGEBRA FACULTY OF MATHEMATICS AND PHYSICS CHARLES UNIVERSITY SOKOLOVSKÁ 83, 186 00 PRAGUE 8 CZECH REPUBLICE-mail: mottet@karlin.mff.cuni.czURL:http://www.karlin.mff.cuni.cz/~mottet/
MICHAEL PINSKER
Affiliation:
DEPARTMENT OF ALGEBRA FACULTY OF MATHEMATICS AND PHYSICS CHARLES UNIVERSITY SOKOLOVSKÁ 83, 186 00 PRAGUE 8 CZECH REPUBLIC INSTITUT FÜR DISKRETE MATHEMATIK UND GEOMETRIE FG ALGEBRA, TU WIEN, VIENNA, AUSTRIAE-mail: marula@gmx.atURL:http://dmg.tuwien.ac.at/pinsker/
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that if an $\omega $ -categorical structure has an $\omega $ -categorical homogeneous Ramsey expansion, then so does its model-complete core.

Keywords

first-order reductRamsey expansionmodel-complete coreomega-categoricityhomogeneous structure

MSC classification

Primary: 03C10: Quantifier elimination, model completeness and related topics
Secondary: 05C55: Generalized Ramsey theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 352 - 361
Check for updates
Copyright
© The Association for Symbolic Logic 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barto, L., Kompatscher, M., Olšák, M., Van Pham, T., and Pinsker, M., The equivalence of two dichotomy conjectures for infinite domain constraint satisfaction problems, Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science—LICS’17, IEEE, 2017, pp. 1–12.10.1109/LICS.2017.8005128CrossRefGoogle Scholar
Barto, L., Kompatscher, M., Olšák, M., Van Pham, T., and Pinsker, M., Equations in oligomorphic clones and the constraint satisfaction problem for $\omega$ -categorical structures. Journal of Mathematical Logic, vol. 19 (2019), no. 2, p. 1950010.10.1142/S0219061319500107CrossRefGoogle Scholar
Barto, L., Opršal, J., and Pinsker, M., The wonderland of reflections. Israel Journal of Mathematics, vol. 223 (2018), no. 1, pp. 363–398.10.1007/s11856-017-1621-9CrossRefGoogle Scholar
Barto, L. and Pinsker, M., The algebraic dichotomy conjecture for infinite domain constraint satisfaction problems, Proceedings of the 31st Annual IEEE Symposium on Logic in Computer Science—LICS’16, Association for Computing Machinery, New York, 2016, pp. 615–622.Google Scholar
Barto, L. and Pinsker, M., Topology is irrelevant. SIAM Journal on Computing, vol. 49 (2020), no. 2, pp. 365–393.10.1137/18M1216213CrossRefGoogle Scholar
Bodirsky, M., Cores of countably categorical structures. Logical Methods in Computer Science (LMCS), vol. 3 (2007), no. 1, pp. 1–16.Google Scholar
Bodirsky, M., New Ramsey classes from old. Electronic Journal of Combinatorics, vol. 21 (2014), no. 2, p. P2.22.10.37236/2566CrossRefGoogle Scholar
Bodirsky, M., Ramsey classes: examples and constructions, Surveys in Combinatorics, London Mathematical Society Lecture Note Series, vol. 424, Cambridge University Press, Cambridge, 2015, pp. 261–293.Google Scholar
Bodirsky, M. and Pinsker, M., Canonical functions: A proof via topological dynamics. Contributions to Discrete Mathematics, to appear.Google Scholar
Bodirsky, M., Pinsker, M., and Pongrácz, A., Projective clone homomorphisms, this Journal (2019), pp. 148–161.Google Scholar
Bodirsky, M., Pinsker, M., and Tsankov, T., Decidability of definability, this Journal, vol. 78 (2013), no. 4, pp. 1036–1054. A conference version appeared in the Proceedings of LICS 2011.Google Scholar
Evans, D. M., Hubička, J., and Nešetřil, J., Automorphism groups and Ramsey properties of sparse graphs. Proceedings of the London Mathematical Society, vol. 119 (2019), pp. 515–546.10.1112/plms.12238CrossRefGoogle Scholar
Hubička, J. and Nešetřil, J., Ramsey Classes with Closure Operations (Selected Combinatorial Applications), Cambridge University Press, Cambridge, 2018, pp. 240–258.Google Scholar
Hubička, J. and Nešetřil, J., All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms). Advances in Mathematics, vol. 356 (2019), p. 106791.10.1016/j.aim.2019.106791CrossRefGoogle Scholar
Kechris, A., Pestov, V., and Todorčević, S., Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups. Geometric and Functional Analysis, vol. 15 (2005), no. 1, pp. 106–189.10.1007/s00039-005-0503-1CrossRefGoogle Scholar
Melleray, J., Van Thé, L. N., and Tsankov, T., Polish groups with metrizable universal minimal flows. International Mathematics Research Notices, vol. 2016 (2015), pp. 1285–1307.10.1093/imrn/rnv171CrossRefGoogle Scholar
Mottet, A. and Pinsker, M., Smooth approximations and CSPs over finitely bounded homogeneous structures, https://arxiv.org/abs/2011.03978, 2020.Google Scholar
Nešetřil, J., Ramsey classes and homogeneous structures. Combinatorics, Probability & Computing, vol. 14 (2005), no. 1–2, pp. 171–189.10.1017/S0963548304006716CrossRefGoogle Scholar
Saracino, D., Model companions for $\ \aleph_0$ -categorical theories. Proceedings of the American Mathematical Society, vol. 39 (1973), pp. 591–598.Google Scholar