Case syncretism is the paradigmatic synthesis of case; multiple case functions are marked by the same form.[1] Case syncretism of articles is the phenomenon in which the inflected form of an adnominal article can express two or more of the case functions attested in the nominal paradigm. For the purpose of this parameter, cases (specific case functions) are considered to be all inflectional categories in which at least some nominally and pronominally inflected forms differ from the rest of the paradigm.
Types:
NoArt: The language does not have articles.
NoCase: The language has articles, but not case marking.
NoArtCase: Case is marked on nouns, not articles.
NoSyncArtCase: The same number of, or more, morphologically unique cases are marked on articles as on nouns, with no occurrence of (independent[2]) syncretism of articles.
SyncArtCase: The same number of, or more, morphologically unique cases are marked on articles as on nouns, with the occurrence of syncretism of articles.[3]
[1] Compare to exponence, which is the syntagmatic synthesis of cases.
[2] The syncretism of nouns does not help when it comes to the syncretism of articles. If nominal case is syncretic and the article consistently shows agreement (i.e., it appears in the same form as the noun for every case function), the article is also syncretic, but this agreement does not indicate specifically article syncretism.
[3] This should be explained in the commentary. (The same number of cases can only occur with case syncretism of articles if the distribution of articles differs from that of nouns.)