The indefinite article is a morpheme that appears alongside a noun in order to mark the noun’s pragmatic indefiniteness. An indefinite entity is one not specifically known to the listener (I saw a dog), or a general representation of the entity, similar to use of ‘any’ (A watched pot never boils).
In terms of marking indefiniteness, languages fall into the following types:
NoArt: The language does not have articles.
NoIndefArt: The language does not have indefinite articles.
Indef=Num: The indefinite article is the numeral ‘one.’[1]
Indef~Num: The indefinite article is not identical to the numeral ‘one,’ but it can be etymologically traced back to that numeral, having since lexicalized into a separate word.
IndefNotNum: The indefinite article bears no resemblance to the numeral ‘one.’
Indef=Aff: Indefiniteness is marked by an affix on the noun.
IndefArt=NonDefArt: Definiteness is a marked feature, while indefiniteness is indicated by the lack of such a marking.[2]
+DoubleIndef: A functional distinction is made between the use of and lack of indefinite articles, such as contrasting the nonspecific and the generic. (This value can only appear alongside the values Indef=Num, IndefNotNum and Indef=Aff.)[3]
[1] Closer examination is often required to determine whether the morpheme appears as a numeral or an article. In many cases, the two uses may overlap and only be distinguished, if at all, by emphasis or word order. In languages that use the word order (syntactic) strategy, this distinction may either be optional or required.
[2] Alternatively, the lack of a definite article may indicate ambiguity, rather than indefiniteness. In such cases, the NoIndefArt type may be a more appropriate classification. In the case of a three-way marking system (definite article vs. indefinite article vs. lack of article), the language will fall into either the Indef=Num, IndefNotNum or Indef=Aff type, supplemented by the +DoubleIndef value.
[3] For example, Hungarian would be considered Indef=Num + DoubleIndef, as evidenced by uses of distinctions such as almát eszik (’[usually,] s/he eats apples’/‘s/he is eating an apple’) ↔ egy almát eszik (‘s/he is eating an apple’) ↔ eszi az almát (‘s/he is eating the apple’).