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Can we ever have $\Gamma \models \perp$? I think since as long as $\Gamma$ has a model, $\Gamma \models \perp$ can never be correct. So it is correct when $\Gamma$ has no model. Is my understanding right?

Thanks in advance!

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That's exactly right: "$\Gamma\models\perp$" is equivalent to "$\Gamma$ has no model" (or "$\Gamma$ is unsatisfiable").

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