STRUCTURE of SUMMABLE TALL IDEALS under KATĚTOV ORDER

Jialiang He; Zuoheng Li; Shuguo Zhang

doi:10.1017/jsl.2023.24

STRUCTURE of SUMMABLE TALL IDEALS under KATĚTOV ORDER

Jialiang He
, Zuoheng Li
, Shuguo Zhang

Sichuan University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that Katětov and Rudin-Blass orders on summable tall ideals coincide. We prove that Katětov order on summable tall ideals is Galois-Tukey equivalent to. It follows that Katětov order on summable tall ideals is upwards directed which answers a question of Minami and Sakai. In addition, we prove that is Borel bireducible to an equivalence relation induced by Katětov order on summable tall ideals.

Original language	English
Pages (from-to)	725-751
Number of pages	27
Journal	Journal of Symbolic Logic
Volume	90
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2023.24
State	Published - 1 Jun 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

Keywords

Galois Tukey connection
Katětov order
summable ideal

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10.1017/jsl.2023.24

Cite this

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abstract = "We show that Kat{\v e}tov and Rudin-Blass orders on summable tall ideals coincide. We prove that Kat{\v e}tov order on summable tall ideals is Galois-Tukey equivalent to. It follows that Kat{\v e}tov order on summable tall ideals is upwards directed which answers a question of Minami and Sakai. In addition, we prove that is Borel bireducible to an equivalence relation induced by Kat{\v e}tov order on summable tall ideals.",

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AU - Li, Zuoheng

AU - Zhang, Shuguo

N1 - Publisher Copyright: © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

PY - 2025/6/1

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N2 - We show that Katětov and Rudin-Blass orders on summable tall ideals coincide. We prove that Katětov order on summable tall ideals is Galois-Tukey equivalent to. It follows that Katětov order on summable tall ideals is upwards directed which answers a question of Minami and Sakai. In addition, we prove that is Borel bireducible to an equivalence relation induced by Katětov order on summable tall ideals.

AB - We show that Katětov and Rudin-Blass orders on summable tall ideals coincide. We prove that Katětov order on summable tall ideals is Galois-Tukey equivalent to. It follows that Katětov order on summable tall ideals is upwards directed which answers a question of Minami and Sakai. In addition, we prove that is Borel bireducible to an equivalence relation induced by Katětov order on summable tall ideals.

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ER -

STRUCTURE of SUMMABLE TALL IDEALS under KATĚTOV ORDER

Abstract

Bibliographical note

Keywords

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