Skip to main content
SpringerLink
Log in

On extendability to \(F_\sigma \) ideals

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

Answering in negative a question of M. Hrušák, we construct a Borel ideal not extendable to any \(F_\sigma \) ideal and such that it is not Katětov above the ideal \(\mathrm {conv}\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

References

  1. Farah, I.: Analytic quotients: theory of liftings for quotients over analytic ideals on the integers. Mem. Am. Math. Soc. 148(702), xvi+177 (2000)

    MathSciNet  MATH  Google Scholar 

  2. Fast, H.: Sur la convergence statistique. Colloq. Math. 2(3–4), 241–244 (1951)

    Article  MathSciNet  Google Scholar 

  3. Filipów, R., Ireneusz, R., Nikodem, M., Piotr, S.: Ideal convergence of bounded sequences. J. Symb. Logic 72(2), 501–512 (2007)

    Article  MathSciNet  Google Scholar 

  4. Fridy, J.A.: On statistical convergence. Analysis 5(4), 301–314 (1985)

    Article  MathSciNet  Google Scholar 

  5. Hrušák, M.: Combinatorics of filters and ideals. Contemp. Math. 533, 29–69 (2011)

    Article  MathSciNet  Google Scholar 

  6. Hrušák, M.: Katětov order on Borel ideals. Arch. Math. Logic 56, 831–847 (2017)

    Article  MathSciNet  Google Scholar 

  7. Just, W., Krawczyk, A.: On certain Boolean algebras \(\cal{P}(\omega )/i\). Trans. Am. Math. Soc. 285(1), 411–429 (1984)

    MathSciNet  MATH  Google Scholar 

  8. Kwela, A.: A note on a new ideal. J. Math. Anal. Appl. 430(2), 932–949 (2015)

    Article  MathSciNet  Google Scholar 

  9. Kwela, A.: Erdős–Ulam ideals vs. simple density ideals. J. Math. Anal. Appl. 462(1), 114–130 (2018)

    Article  MathSciNet  Google Scholar 

  10. Kwela, A., Tryba, J.: Homogeneous ideals on countable sets. Acta Math. Hung. 151, 139–161 (2016)

    Article  MathSciNet  Google Scholar 

  11. Meza-Alcántara, D.: Ideals and filters on countable set. Ph.D. thesis, Universidad Nacional Autónoma de México (2009)

  12. Steinhaus, H.: Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2, 73–74 (1951)

    Google Scholar 

  13. Šalát, T.: On statistically convergent sequences of real numbers. Math. Slovaca 30(2), 139–150 (1980)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, ul. Wita Stwosza 57, 80-308, Gdańsk, Poland

    Adam Kwela

Authors
  1. Adam Kwela
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adam Kwela.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kwela, A. On extendability to \(F_\sigma \) ideals. Arch. Math. Logic 61, 881–890 (2022). https://doi.org/10.1007/s00153-022-00822-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-022-00822-w

Keywords

Mathematics Subject Classification

Search

Navigation