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sav08:simple_qe_for_dense_linear_orders [2009/04/21 19:34] vkuncak |
sav08:simple_qe_for_dense_linear_orders [2009/04/21 23:59] vkuncak |
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| Formulas $T$ are the formulas that are closed formulas that are true in the structure $(\mathbb{Q},<)$ or rational numbers. | Formulas $T$ are the formulas that are closed formulas that are true in the structure $(\mathbb{Q},<)$ or rational numbers. | ||
| + | |||
| + | **Example:** | ||
| + | \[ | ||
| + | \forall x. \exists y.\ x < y \ \land\ (\forall z. (x < z \rightarrow z=y \lor y < z) | ||
| + | \] | ||
| + | Is this formula true in dense linear orders? Is there a non-dense linear order where its truth value is different? | ||
| ===== Normal form of Formulas ===== | ===== Normal form of Formulas ===== | ||