Journal of Symbolic Logic

Coordinatisation by binding groups and unidimensionality in simple theories

Ziv Shami

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Abstract

In a simple theory with elimination of finitary hyperimaginaries if tp(a) is real and analysable over a definable set Q, then there exists a finite sequence (ai | i≤ n*)⊆ dcleq(a) with an*=a such that for every i≤ n*, if pi=tp(ai/{aj | j<i}) then Aut(pi/Q) is type-definable with its action on pi𝒞. A unidimensional simple theory eliminates the quantifier ∃ and either interprets (in 𝒞eq) an infinite type-definable group or has the property that ACL(Q)=𝒞 for every infinite definable set Q.

Article information

Source
J. Symbolic Logic, Volume 69, Issue 4 (2004), 1221-1242.

Dates
First available in Project Euclid: 2 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1102022220

Digital Object Identifier
doi:10.2178/jsl/1102022220

Mathematical Reviews number (MathSciNet)
MR2135664

Zentralblatt MATH identifier
1081.03030

Citation

Shami, Ziv. Coordinatisation by binding groups and unidimensionality in simple theories. J. Symbolic Logic 69 (2004), no. 4, 1221--1242. doi:10.2178/jsl/1102022220. https://projecteuclid.org/euclid.jsl/1102022220


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