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sav08:compactness_for_first-order_logic [2008/03/20 17:51] vkuncak |
sav08:compactness_for_first-order_logic [2008/03/20 17:55] vkuncak |
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| ====== Compactness for First-Order Logic ====== | ====== Compactness for First-Order Logic ====== | ||
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| + | **Theorem (Compactness for First-Order Logic):** If every finite subset of a set $S_0$ of first-order formulas has a model, then $S_0$ has a model. | ||
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| + | **Proof:** | ||
| Let $S_0$ be a set of first-order formulas. | Let $S_0$ be a set of first-order formulas. | ||
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| Therefore $S_3$ has no model. | Therefore $S_3$ has no model. | ||
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| + | **End of Proof.** | ||