Is there a difference between the two ways to express an indirect object, as is described in the “personal objective pronouns” section? E.g. between »του δείχνω το πουκάμισο» and «δείχνω το πουκάμισο σε αυτόν» , is one “more correct” or is there a different emphasis?
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του vs σε αυτόν
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A0Re: του vs σε αυτόν
Like you suggest, if you use σε αυτόν, that normally conveys emphasis - it communicates something like "I showed the shirt to him specifically, not to some other person".
Both του and σε αυτόν are "correct", although if you overused σε αυτόν in situations where emphasis isn't needed, I think it might sound a bit unnatural.
However, if the indirect object is a noun rather than a pronoun, the σε form is more neutral. "I show the shirt to my brother" -> "Δείχνω το πουκάμισο στον αδελφό μου", with no special emphasis.
This thread might be useful too, especially O.Zoe's answer (which is about indirect objects in general even though the thread started with the verb αρέσω): viewtopic.php?p=25269-σε-with-verb-αρέσω