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Interpretable Groups, Stably Embedded Sets, and Vaughtian Pairs
Author(s) -
Herwig Bernhard,
Hrushovski Ehud,
Macpherson Dugald
Publication year - 2003
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/s0024610703004423
Subject(s) - countable set , unary operation , predicate (mathematical logic) , categorical variable , mathematics , group (periodic table) , combinatorics , discrete mathematics , computer science , physics , statistics , quantum mechanics , programming language
The paper concerns sufficiently saturated structures M over a countable language with a unary predicate P . It is shown that if P ( M )is stably embedded and there are no Vaughtian pairs with respect to P , then an infinite group is interpretable over M (in an infinitary sense of ‘interpretable’). Also, it is shown that if M is ω‐categorical, f : D → P is a 0‐definable map with finite fibres, and P ( M ) is stably embedded but D is not, then some infinite group is first‐order interpretable over M .