Finiteness of  U ‐rank implies simplicity in homogeneous structures | Zendy

Hyttinen Tapani | Zendy

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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)

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