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In the phrase dem alten Hafenviertel, I have dem which is dativ of der or das, then I have alten which I suppose is the accusative of der and, at the end, I have the noun Hafenviertel which has the member das.

Can someone explain to me how is this construction is even valid?

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check the "Schwache Flektion" section: "alten" is actually dative – Vogel612 Feb 27 '14 at 8:16
you cannot tell what case you're looking at based on adjective endings. Alten can be Accusative, Dative, Genetive and Nominative... it depends on gender and number. – Emanuel Feb 27 '14 at 10:45

2 Answers 2

-en at the end of an adjective doesn't imply it's accusative. There's lot of -en not concerning Akk.

See schwache Deklination in this table.

Dem alten Hafenviertel

is purely Dative. Addressing the last question, strictly speaking, that construction is valid because it's the only possible correct construction.

But that doesn't really help. Maybe what you want to know is the following. Given a chain of a determiner (see link bellow), an adjective and a noun:

Det. Adj Nomen

you might want to know, which ending does the adjective bear?

First choose according to this table the type of declension your determiner induces: you have three options, namely, strong, weak and mixed. (in your example, it was das – as you stated). Then GOTO the inflection table itself and, first according to whether you have strong, weak or mixed, pick a table (in your case, weak declension). Then pick your entry according to the gender and case (in your example, neutr. and dative, signaled with stars bellow; little arrows point to the right ending).

   Schwache Flexion (mit bestimmtem Artikel)
           Maskulin     Neutrum*      Feminin       Plural

 Nominativ  der alte    das alte    die alte    die alten 
  Akkusativ den alten   das alte    die alte    die alten 
   Dativ*   dem alten  →dem alten←  der alten   den alten 
  Genitiv   des alten   des alten   der alten   der alten 
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you should explain the difference between the flection types. – Vogel612 Feb 27 '14 at 10:04
@Vogel612 2? There are three, oder? (ohne Artikel, mit bestimmt. Art., mit unbestimmt. Art) – c.p. Feb 27 '14 at 10:05
corrected that.. well you could just link to a question here on GLU, i bet you can find one with a good and concise explanation ;) – Vogel612 Feb 27 '14 at 10:06

Accusative wouldn't use an -n ending:

Die Zeitungen schreiben viel über das alte Hafenviertel.

No alten used at all here in the accusative case.

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