- English only

# Lab for Automated Reasoning and Analysis LARA

# 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] (current) 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. |