On the Denjoy rank, the Kechris-Woodin rank and the Zalcwasser rank
Haseo Ki · Transactions of the American Mathematical Society · 1997
We show that the Denjoy rank and the Zalcwasser rank are incomparable. We construct for any countable ordinal α \alpha differentiable functions f f and g g such that the Zalcwasser rank and the Kechris-Woodin rank of f f are α + 1 \alpha +1 but the Denjoy rank of f f is 2 and the Denjoy rank and the Kechris-Woodin rank of g g are α + 1 \alpha +1 but the Zalcwasser rank of g g is 1. We then derive a theorem that shows the surprising behavior of the Denjoy rank, the Kechris-Woodin rank and the Zalcwasser rank.