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The Hrushovski property for hypertournaments and profinite topologies
Author(s) -
Huang Jingyin,
Pawliuk Micheal,
Sabok Marcin,
Wise Daniel T.
Publication year - 2019
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12244
Subject(s) - disjoint sets , corollary , pairwise comparison , property (philosophy) , extension (predicate logic) , mathematics , combinatorics , discrete mathematics , pure mathematics , computer science , statistics , epistemology , philosophy , programming language
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.