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However, it could reuse e#0 (denoting 'a in place of e#1 (denoting the existential quantifier). This would introduce an unnecessary identification between e#0 and e#1, resulting in a model that is not homomorphically minimal:
The core idea is to avoid introducing new elements to the model when possible. Here is an example for the simple case:
Razor currently builds the following model for this theory:
However, it could reuse
e#0
(denoting'a
in place ofe#1
(denoting the existential quantifier). This would introduce an unnecessary identification betweene#0
ande#1
, resulting in a model that is not homomorphically minimal:However, this kind of element reuse often helps avoid constructing infinite models as for the case for the grandpa example.
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