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I know this is quite the dumb question, but I was wondering what the correct usage of adjectives when in genitive was. My confusion stems from the following sentence on the Axiom of Choice (Auswahlaxiom): Für jede Menge nichtleerer Mengen gibt es eine Auswahlfunktion.
Now, as I understand it, the "nichtleerer" here is written so as it is declined in genitive (with regard to the plural "Mengen") and is to be interpreted as a "For every set of non-empty sets...".
My question is then, which of the following would be correct: "Grundkategorien politischer Ökonomie", or "Grundkategorien der politischen Ökonomie"? My guess goes towards the second (as one would, for example, have a "Kritik der reinen Vernunft" and not a "Kritik reiner Vernunft", I assume). But why is that so? When should the determinate article be included/utilized in the presence of an adjective and genitive and when can one write something akin to the first sentence here presented?
I can maybe guess that it might have something to do with the relations of pertaining (as in, this is a set (made up) of X versus this is the critique of Y) but I don't really have any particularly strong notion there and I would wonder how one differentiates then between a need to use the genitive + determinate article and, say, a "von" to indicate it is "of" something.
Thus, any help is much welcomed and appreciated!

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This isn't about adjectives at all. Or about genitive. But about definiteness.

  • Grundkategorien politischer Ökonomie

This is indefinite and not exactly one. Hence no article. What this conveys is that there are many political economies, and they share those basic categories. This is likely what is meant. (It doesn't matter that Ökonomie isn't plural. The indefiniteness alone makes us think about Ökonomie as a somewhat broad topic.)

  • Grundkategorien der politischen Ökonomie

This on the other hand is definite. This conveys there is exactly one political economy and it has some basic categories.

  • Grundkategorien einer politischen Ökonomie

This is again indefinite but exactly one. It conveys there are many political economies from which we randomly pick one and its basic categories.

And the same for your other examples.

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