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Finiteness of U ‐rank implies simplicity in homogeneous structures
Author(s) -
Hyttinen Tapani
Publication year - 2003
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.200310062
Subject(s) - corollary , rank (graph theory) , mathematics , simple (philosophy) , homogeneous , property (philosophy) , extension (predicate logic) , simplicity , set (abstract data type) , combinatorics , characterization (materials science) , type (biology) , pure mathematics , computer science , physics , philosophy , epistemology , optics , programming language , ecology , quantum mechanics , biology
A (large) superstable homogeneous structure is said to be simple if every complete type over any set A has a free extension over any B ⊇ A . In this paper we give a characterization for this property in terms of U ‐rank. As a corollary we get that if the structure has finite U ‐rank, then it is simple. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)