anarchy as an idea was always horizontal government structure built on decentralised syndicates and communes

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Your ancient Greek sucks, bruv.

https://www.etymonline.com/word/anarchy#etymonline_v_13397

1530s, "absence of government," from French anarchie or directly from Medieval Latin anarchia, from Greek anarkhia "lack of a leader, the state of people without a government" (in Athens, used of the Year of Thirty Tyrants, 404 B.C., when there was no archon), abstract noun from anarkhos "rulerless," from an- "without" (see an- (1)) + arkhos "leader" (see archon).