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Unimodular Minimal Structures
Author(s) -
Hrushovski Ehud
Publication year - 1992
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/s2-46.3.385
Subject(s) - unimodular matrix , mathematics , combinatorics , domain (mathematical analysis) , discrete mathematics , range (aeronautics) , type (biology) , pure mathematics , mathematical analysis , ecology , materials science , composite material , biology
A strongly minimal structure D is called unimodular if any two finite‐to‐one maps with the same domain and range have the same degree; that is if f i : U → V is everywhere k i to‐l, then k 1 = k 2 ,. THEOREM. Unimodular strongly minimal structures are locally modular. This extends Zil'ber's theorem on locally finite strongly minimal sets, Urbanik's theorem on free algebras with the Steinitz property, and applies also to minimal types in ℵ 0 ‐categorical stable theories.