This paper concerns the relation between parameterized first order data types and first order logic. Augmenting first order logic by data type definitions yields in general a strictly stronger logic than first order logic. We consider some properties of the new logic for fixed data type definitions. While our new logic always fulfills the downward Skolem-Löwenheim property, compactness is fulfilled if and only if for the given data type definition the new logic has the same expressive power than first order logic. We show that this last property is undecidable.
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