"Personal a" refers specifically to the phenomenon of using the preposition "a" to mark the direct object of a transitive verb.
A good general rule for beginning students is: if the direct object is an identifiable person or an identifiable set of people (or a being or beings one thinks of as being "people", such as pets, supernatural beings, and so on), using "personal a" is almost always required. Otherwise, one almost never uses "personal a" to mark the direct object.
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