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The Robinson property and amalgamations of higher arities
Author(s) -
Nyiri David
Publication year - 2016
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201500027
Subject(s) - property (philosophy) , mathematics , homogeneous , relation (database) , series (stratigraphy) , binary relation , order (exchange) , pure mathematics , algebra over a field , discrete mathematics , combinatorics , computer science , epistemology , paleontology , philosophy , finance , economics , biology , database
In this article we discuss a version of the Robinson property studied recently by Gyenis in [3][Z. Gyenis, 2014], and we present a solution to one of his open problems. We say that a first‐order structure M satisfies the Robinson property whenever the union of two non‐trivial partial n ‐types over different finite sets is realizable if and only if they are not explicitly contradictory. In his article, Gyenis showed that a universal, homogeneous structure over a language that consists of at most binary relation symbols satisfies the Robinson property if and only if its age has a generalized amalgamation property (the so called prescribed amalgamation property, PAP). We go further and define a series of new kinds of amalgamation properties, AP n for any natural number n . Using these properties we can characterize all universal and homogeneous structures that satisfy the Robinson property independently from the arities of relation symbols of the language.