Summary

Yosef Karo Translation:Shulchan Aruch — Orach Chaim 586…

If one intended to claim ownership of the shofar, they have not fulfilled their obligation, as it is now an object of idol worship owned by a Jew. (There are those who are stringent and who regard even blowing a shofar [that is an object of idol worship] owned by an idol worshipper as fulfilling their obligation unless the shofar's status as an object of idol worship was nullified before the holiday (Mordechai) .
Source: Wikisource

Yosef Karo Translation:Shulchan Aruch — Orach Chaim 586…

Having a non-Jew do these things is permissible, because that is a rabbinic prohibition on top of a rabbinic prohibition. (Meaning, the prohibition of telling a non-Jew to do an action [on a holiday] that is prohibited by the Torah is a rabbinically enacted prohibition to ensure resting [shevut] from telling non-Jews to do things, and when the action in question is itself a rabbinic prohibition, this is a rabbinic prohibition on top of a rabbinic prohibition [shevut d'shevut] ) and when there is a commandment to do, the rabbis made no such decree (see 307) .
Source: Wikisource

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