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sav08:extending_languages_of_decidable_theories [2008/04/15 14:26] vkuncak |
sav08:extending_languages_of_decidable_theories [2008/04/15 14:27] vkuncak |
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| **Proof:** | **Proof:** | ||
| + | How to define $L'$? | ||
| ++++| | ++++| | ||
| Fix an ordering on the set $V$ of all first-order variables. If $G$ is a term, formula, or a set of formulas, let $fv(G)$ denote the ordered list of its free variables. | Fix an ordering on the set $V$ of all first-order variables. If $G$ is a term, formula, or a set of formulas, let $fv(G)$ denote the ordered list of its free variables. | ||
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| T' = \{ F \mid rf(F) \in Conseq(T) \} | T' = \{ F \mid rf(F) \in Conseq(T) \} | ||
| \] | \] | ||
| + | ++++ | ||
| + | How to do quantifier elimination in $T'$? | ||
| + | ++++| | ||
| The quantifier-free version of $F$ is then simply $R_{rf(F)}(x_1,\ldots,x_n)$ where $fv(rf(F)) = x_1,\ldots,x_n$. This quantifier elimination is easy and effective (and trivial). | The quantifier-free version of $F$ is then simply $R_{rf(F)}(x_1,\ldots,x_n)$ where $fv(rf(F)) = x_1,\ldots,x_n$. This quantifier elimination is easy and effective (and trivial). | ||
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| ++++ | ++++ | ||