Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
sav08:quantifier_elimination_definition [2009/04/22 10:07] vkuncak |
sav08:quantifier_elimination_definition [2009/04/22 10:07] vkuncak |
||
|---|---|---|---|
| Line 11: | Line 11: | ||
| If we look at one interpretation, then ${\cal I}$ contains only that interpretation and the condition $\models F$ means $e_F(F)(I)$. | If we look at one interpretation, then ${\cal I}$ contains only that interpretation and the condition $\models F$ means $e_F(F)(I)$. | ||
| - | **Shorthand:** We will be fixing $T$ and write $\models F$ as a shorthand for $T \models F$. | + | **Shorthand:** We will generally fix $T$ and write $\models F$ as a shorthand for $T \models F$. |
| **Example:** Let $M = ({\cal Z},+)$ be the structure of integers with addition. If we let ${\cal I} = \{ M \}$ then $T$ in the definition above is the set of all formulas involving only $+$ that are true about integers. In this example, | **Example:** Let $M = ({\cal Z},+)$ be the structure of integers with addition. If we let ${\cal I} = \{ M \}$ then $T$ in the definition above is the set of all formulas involving only $+$ that are true about integers. In this example, | ||