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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)2845-2870
Number of pages26
JournalTransactions of the American Mathematical Society
Volume349
Issue number7
Publication statusPublished - 1997 Dec 1

Fingerprint

Differentiate
Countable
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

@article{a04a64ea4d154b0a820b2675f1b1ac35,
title = "On the denjoy rank, the kechris-woodin rank and the zalcwasser rank",
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.",
author = "Haseo, {K. I.}",
year = "1997",
month = "12",
day = "1",
language = "English",
volume = "349",
pages = "2845--2870",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "7",

}

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

In: Transactions of the American Mathematical Society, Vol. 349, No. 7, 01.12.1997, p. 2845-2870.

Research output: Contribution to journalArticle

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 -