Abstract
We prove that a ‘small’ extension of a minimal AF equivalence relation on a Cantor set is orbit equivalent to the AF relation. By a ‘small’ extension we mean an equivalence relation generated by the minimal AF equivalence relation and another AF equivalence relation which is defined on a closed thin subset. The result we obtain is a generalization of the main theorem in [GMPS2]. It is needed for the study of orbit equivalence of minimal Z d -systems for d>2 [GMPS3], in a similar way as the result in [GMPS2] was needed (and sufficient) for the study of minimal Z 2 -systems [GMPS1].
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