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Greek language, culture, and religions,
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different religions and the syncretism,
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Greek education, the polis structure --
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all of these things remained in the East throughout
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the Roman rule of the East, all the way up until the time
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you had a Christian emperor with Constantine, and later.
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But there's one thing that the Romans made even more of,
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than the Greeks had made of, and this is the patron-client structure.
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This is a bit more of a distinctly Roman institution,
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even a legal institution.
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But it's important for understanding both the Roman empire,
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as well as early Christianity and its patron-client relations.