Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | |||
sav08:compactness_for_first-order_logic [2008/03/20 17:57] vkuncak |
sav08:compactness_for_first-order_logic [2008/03/20 17:58] vkuncak |
||
---|---|---|---|
Line 11: | Line 11: | ||
Then $expandProp(clauses(S_0))$ has no model. | Then $expandProp(clauses(S_0))$ has no model. | ||
- | Some finite subset $S_1 \subseteq expandProp(clauses(S_0))$ of it has no model. | + | Then by [[Compactness Theorem]] for propositional logic, some finite subset $S_1 \subseteq expandProp(clauses(S_0))$ of it has no model. |
There is then finite subset of clauses $S_2 \subseteq clauses(S_0)$ that generate $S_1$, i.e. such that $S_1 \subseteq expandProp(S_2)$. Therefore, $S_2$ has no model. | There is then finite subset of clauses $S_2 \subseteq clauses(S_0)$ that generate $S_1$, i.e. such that $S_1 \subseteq expandProp(S_2)$. Therefore, $S_2$ has no model. |