## On the Denjoy rank, the Kechris-Woodin rank and the Zalcwasser rank

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**349**(1997), 2845-2870 Request permission

## Abstract:

We show that the Denjoy rank and the Zalcwasser rank are incomparable. We construct for any countable ordinal $\alpha$ differentiable functions $f$ and $g$ such that the Zalcwasser rank and the Kechris-Woodin rank of $f$ are $\alpha +1$ but the Denjoy rank of $f$ is 2 and the Denjoy rank and the Kechris-Woodin rank of $g$ are $\alpha +1$ but the Zalcwasser rank of $g$ is 1. We then derive a theorem that shows the surprising behavior of the Denjoy rank, the Kechris-Woodin rank and the Zalcwasser rank.## References

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## Additional Information

**Haseo Ki**- Affiliation: Department of Mathematics, Yonsei University, Seoul, 120-749, Korea
- Email: haseo@bubble.yonsei.ac.kr
- Received by editor(s): April 13, 1995
- Received by editor(s) in revised form: January 18, 1996
- Additional Notes: Partially supported by GARC-KOSEF
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**349**(1997), 2845-2870 - MSC (1991): Primary 04A15, 26A21; Secondary 42A20
- DOI: https://doi.org/10.1090/S0002-9947-97-01767-4
- MathSciNet review: 1390042