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Some Structural Aspects of the Katětov Order on Borel Ideals

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Abstract

We prove that the Katětov order on Borel ideals (1) contains a copy of \(\mathcal {P}(\omega )/\mathbf {Fin}\), consequently it has increasing and decreasing chains of lenght 𝔟; (2) the sequence F i n α (α < ω 1) is a strictly increasing chain; and (3) in the Cohen model, Katětov order does not contain any increasing nor decreasing chain of length 𝔠, answering a question of Hrušák (2011).

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Authors and Affiliations

  1. Centro de Ciencias Matemáticas UNAM, Morelia, Mexico

    Osvaldo Guzmán-González

  2. Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio Alpha, Ciudad Universitaria, 58060, Morelia, Michoacán, México

    David Meza-Alcántara

Authors
  1. Osvaldo Guzmán-González
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  2. David Meza-Alcántara
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Correspondence to David Meza-Alcántara.

Additional information

Second author was supported by grants UMSNH-CIC-9.30 and CONACYT-CB-169078

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Guzmán-González, O., Meza-Alcántara, D. Some Structural Aspects of the Katětov Order on Borel Ideals. Order 33, 189–194 (2016). https://doi.org/10.1007/s11083-015-9358-8

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  • DOI: https://doi.org/10.1007/s11083-015-9358-8

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