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:first-order_theories [2008/03/19 15:13] vkuncak |
sav08:first-order_theories [2008/03/19 22:02] damien |
||
|---|---|---|---|
| Line 30: | Line 30: | ||
| Let $T = Conseq(\{Ref,Sym,Tra\})$. Let us answer the following: | Let $T = Conseq(\{Ref,Sym,Tra\})$. Let us answer the following: | ||
| * Is $T$ ++consistent?|Yes, take, for example, ordering on integers.++ | * Is $T$ ++consistent?|Yes, take, for example, ordering on integers.++ | ||
| - | * Is $T$ ++complete?|No, take, for example, $\exists x. \forall y. x \le y$.++ | + | * Is $T$ ++complete?|No, take, for example, $\exists x. \forall y. x \le y$. It is true with the ordering on $\mathbb{N}$, but false with the ordering on $\mathbb{Z}$.++ |