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If $\\mathbb{D}$ is a subset of $\\mathbb{M}$, following D. Zambella we consider $e(\\mathbb{D})=\\{\\mathbb{D}^\\prime\\mid (\\mathbb{M},\\mathbb{D})\\equiv (\\mathbb{M},\\mathbb{D}^\\prime)\\}$ and $o(\\mathbb{D})=\\{\\mathbb{D}^\\prime\\mid (\\mathbb{M},\\mathbb{D})\\cong (\\mathbb{M},\\mathbb{D}^\\prime)\\}$. The general question we ask is when $e(\\mathbb{D})=o(\\mathbb{D})$ ? The case where $\\mathbb{D}$ is $A$-invariant for some small set $A$ is rather straightforward: it just mean that $\\mathbb{D}$ is definable. 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