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Journal of the London Mathematical Society 1992 s2-46(3):385-396; doi:10.1112/jlms/s2-46.3.385
© 1992 by London Mathematical Society
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© Oxford University Press

Unimodular Minimal Structures

Ehud Hrushovski

Department of Mathematics MIT 2-277, Cambridge, MA 02139, USA

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 fi: U -> V is everywhere ki to-l, then k1 = k2.

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 N0-categorical stable theories.

Department of Mathematics, The Hebrew University, Jerusalem, Israel


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