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Elimination of imaginaries in expansions of o-minimal structures by generic sets. (English) Zbl 1108.03045

Let \(T\) be an o-minimal theory and let \(T_p\) be obtained by adding a generic predicate. The author shows: If \(T\) is o-minimal and elimininates imaginaries, then \(T_p\) also eliminates imaginaries. The paper also contains a characterization of the unary relations definable in expansions of o-minimal structures by generic sets.

MSC:

03C64 Model theory of ordered structures; o-minimality
Full Text: DOI

References:

[1] Tame topology and o-minimal structures (1998) · Zbl 0953.03045
[2] A course in model theory (2000)
[3] Fundamenta Mathematicae pp 193– (1999) · Zbl 0933.00004
[4] Model theory and algebraic geometry: An introduction to E. Hrushovski’s proof of the Geometric Mordell-Lang Conjecture pp 19– (1998)
[5] Model theory (1993)
[6] Annals of Pure and Applied Logic pp 71– (1998)
[7] Logic Colloquium ’01 (Vienna) 20 pp 281– (2005)
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