Coordinatisation by binding groups and unidimensionality in simple theories

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 (a_i | i≤ n^*)⊆ dcl^eq(a) with a_n^*=a such that for every i≤ n^*, if p_i=tp(a_i/{a_j | j<i}) then Aut(p_i/Q) is type-definable with its action on p_i^𝒞. A unidimensional simple theory eliminates the quantifier ∃^∞ and either interprets (in 𝒞^eq) an infinite type-definable group or has the property that ACL(Q)=𝒞 for every infinite definable set Q.