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We show that the Borel hierarchy of the class of context free ω-languages, or even of the class of ω-languages accepted by Büchi 1-counter automata, is the same as the Borel hierarchy of the class of ω-languages accepted by Turing machines with a Büchi acceptance condition. In particular, for each recursive non null ordinal α, there exist some Σ 0 α -complete and some Π 0 α -complete ω-languages accepted by Büchi 1counter automata. And the supremum of the set of Borel ranks of context freedoi:10.1017/s0960129506005597 fatcat:g3jri3nlt5aurozzy5neishngy