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 (ω^ω, ≤^∗). It follows that Katětov order on summable tall ideals is upwards directed which answers a question of H. Minami and H. Sakai. In addition, we prove that l_∞ is Borel bireducible to an equivalence relation induced by Katětov order on summable tall ideals.

Original language	English
Journal	Journal of Symbolic Logic
DOIs	https://doi.org/10.1017/jsl.2023.24
State	Accepted/In press - 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 Cambridge University Press. All rights reserved.

Keywords

Galois-Tukey connection
Katětov order
Summable ideal

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10.1017/jsl.2023.24

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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 (ωω, ≤∗). It follows that Kat{\v e}tov order on summable tall ideals is upwards directed which answers a question of H. Minami and H. Sakai. In addition, we prove that l∞ is Borel bireducible to an equivalence relation induced by Kat{\v e}tov order on summable tall ideals.",

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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 (ωω, ≤∗). It follows that Katětov order on summable tall ideals is upwards directed which answers a question of H. Minami and H. Sakai. In addition, we prove that l∞ is Borel bireducible to an equivalence relation induced by Katětov order on summable tall ideals.

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Structure of summable tall ideals under Katětov order

Abstract

Bibliographical note

Keywords

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