### Abstract

We show that the Denjoy rank and the Zalcvasser rank are incomparable. We construct for any countable ordinal α differentiate functions f and g such that the Zalcwasser rank and the Kechris-Woodin rank of f are α + 1 but the Denjoy rank of f is 2 and the Denjoy rank and the KechrisWoodin rank of g are α + 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.

Original language | English |
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Pages (from-to) | 2845-2870 |

Number of pages | 26 |

Journal | Transactions of the American Mathematical Society |

Volume | 349 |

Issue number | 7 |

Publication status | Published - 1997 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Transactions of the American Mathematical Society*, vol. 349, no. 7, pp. 2845-2870.

**On the denjoy rank, the kechris-woodin rank and the zalcwasser rank.** / Haseo, K. I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the denjoy rank, the kechris-woodin rank and the zalcwasser rank

AU - Haseo, K. I.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - We show that the Denjoy rank and the Zalcvasser rank are incomparable. We construct for any countable ordinal α differentiate functions f and g such that the Zalcwasser rank and the Kechris-Woodin rank of f are α + 1 but the Denjoy rank of f is 2 and the Denjoy rank and the KechrisWoodin rank of g are α + 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.

AB - We show that the Denjoy rank and the Zalcvasser rank are incomparable. We construct for any countable ordinal α differentiate functions f and g such that the Zalcwasser rank and the Kechris-Woodin rank of f are α + 1 but the Denjoy rank of f is 2 and the Denjoy rank and the KechrisWoodin rank of g are α + 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.

UR - http://www.scopus.com/inward/record.url?scp=33646885769&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646885769&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33646885769

VL - 349

SP - 2845

EP - 2870

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 7

ER -