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We call \u03b1 \u03b2-relations our alternative versions of \u03bb-theories. We also clarify the actual role of \u03b1-renaming in the lambda calculus: it expresses a property of extensionality for a certain class of terms. To motivate the necessity of \u03b1-renaming, we construct an unusual denotational model of the lambda calculus that validates all structural and beta conditions but not \u03b1-renaming. 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