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sav08:isomorphism_of_interpretations [2008/03/19 17:23] vkuncak |
sav08:isomorphism_of_interpretations [2008/03/20 13:37] vkuncak |
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| **Lemma:** If $s$ is isomorphism from $I_1$ to $I_2$, then for every first-order term $t$ we have | **Lemma:** If $s$ is isomorphism from $I_1$ to $I_2$, then for every first-order term $t$ we have | ||
| \[ | \[ | ||
| - | s(e_T(I_1)(t))=e_T(I_2)(t) | + | s(e_T(t)(I_1))=e_T(t)(I_2) |
| \] | \] | ||
| - | and for every first-order logic formula $F$ we have $e_F(I_1)(F)=e_F(I_2)(F)$. | + | and for every first-order logic formula $F$ we have $e_F(F)(I_1)=e_F(F)(I_2)$. |
| - | **Proof:** | + | **Proof:** ++++|Induction on the structure of terms and formulas. |
| - | ++++|Induction on the structure of terms and formulas. | + | |
| + | Case for $F_1 \land F_2$. | ||
| + | Case for $\exists x.F$. Induction issues, function update on isomorphic interpretations. | ||
| ++++ | ++++ | ||