The Hrushovski property for hypertournaments and profinite topologies

Huang, Jingyin; Pawliuk, Michael; Sabok, Marcin; Wise, Daniel

doi:10.1112/jlms.12244

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Journal Article

The Hrushovski property for hypertournaments and profinite topologies

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Huang, Jingyin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/jlms.12244
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arXiv:1809.06435.pdf
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Citation

Huang, J., Pawliuk, M., Sabok, M., & Wise, D. (2019). The Hrushovski property for hypertournaments and profinite topologies. Journal of the London Mathematical Society, 100(3), 757-774. doi:10.1112/jlms.12244.

Cite as: https://hdl.handle.net/21.11116/0000-0005-5BF8-E

Abstract

We study the problem of extending partial isomorphisms for hypertournaments, which are relational structures generalizing tournaments. This is a generalized version of an old question of Herwig and Lascar. We show that the generalized problem has a negative answer, and we provide a positive answer in a special case. As a corollary, we show that the extension property holds for tournaments in case the partial isomorphisms have pairwise disjoint ranges and pairwise disjoint domains.