Paris models are rigid when their complete theory has a well-founded model
= Paris models are rigid when their complete theory has a well-founded model
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Under the hypothesis of <Paris models are well-founded when their complete theory has a well-founded model>, a Paris model $M$ is well-founded. Every automorphism of $M$ is then the identity by external <epsilon induction>: once all members of $x$ are fixed, extensionality gives $\pi(x)=\{\pi(y):y\in^M x\}=x$. Hence $M$ is a <rigid first-order structure>.