Have a personal or library account? Click to login
P-Like Properties of Meager Ideals and Cardinal Invariants Cover

P-Like Properties of Meager Ideals and Cardinal Invariants

By: Adam Marton  
Open Access
|Nov 2023

References

  1. HAGA, K. B.—SCHRITTESSER, D.—TÖRNQUIST, A.: MAD families, determinacy, and forcing, J. Math. Log. 22 (2021), no. 1, 2150026.
  2. BARTOSZYƃSKI, T.—JUDAH, H.: Set Theory: On the Structure of the Real Line. CRC Press (Taylor & Francis Group) London, 1995
  3. BLASS, A.: Combinatorial cardinal characteristics of the continuum, In: (M. Foreman, A. Kanamori, eds.), Handbook of Set Theory. Springer-Verlag, Berlin 2010, pp. 395–489.
  4. BUKOVSKÁ, Z.: Thin sets in trigonometrical series and quasinormal convergence,Math. Slovaca 40 (1990), no. 1, 53–62.
  5. Császár,Á.—Laczkovich, M. Discrete and equal convergence, Stud. Sci. Math. Hungar. 10 (1975), 463–472.
  6. FARKAS, B.: Combinatorics of Borel Ideals Ph.D. Thesis, Budapest University of Technology and Economics Department of Algebra, Institute of Mathematics Supervisor: Prof. Lajos Soukup, Alfréd Rényi Institute of Mathematics Hungarian Academy of Sci. 2011.
  7. FARKAS, B.—SOUKUP, L.: More on cardinal invariants of analytis P-ideals, Commentationes Mathematicae Universitatis Carolinae 50 (2009), no. 2, 281–295.
  8. FARKAS, B.—ZDOMSKYY, L.: Ways of destruction, J. Symb. Log. 87 (2022), no. 3, 938–966.
  9. FILIPÓW, R.—STANISZEWSKI, M.: On ideal equal convergence, Cent. Eur. J. Math. 12 (2014), no. 6, 896–910.
  10. R. FILIPÓW, R.—STANISZEWSKI, M.: Pointwise versus equal (quasi-normal) convergence via ideals, J. Math. Anal. Appl. 422 (2015), no. 2, 995–1006.
  11. R. FILIPÓW, R.—SZUCA, P.: Three kinds of convergence and the associated ℐ-Baire classes, J. Math. Anal. Appl. 391 (2012), no. 1, 1–9.
  12. GUZMÁN-GONZÁLEZ, O.—HRUƠÁK, M.— MARTÍNEZ-RANERO, C. A.—RAMOS-GARÍA, U. A.: Generic existence of MAD families, J. Symb. Log. 82 (2017), no. 1, 303–316.
  13. HALBEISEN, L.J.: Combinatorial Set Theory With a Gentle Introduction to Forcing. Springer-Verlag, Berlin, 2012.
  14. HERNÁNDEZ-HERNÁNDEZ, F.—HRUƠÁK, M.: Cardinal invariants of analytic P-ideals, Canad. J. Math. 59 (2007), no. 3, 575–595.
  15. HRUƠÁK, M.: Combinatorics of filters and ideals, Contemp. Math. 533 (2011), 29–69.
  16. HRUƠÁK, M.: Katětov order on Borel ideals, Arch. Math. Logic 56 (2017), no. 3, 831–847.
  17. HRUƠÁK, M.—GARĆIA-FERREIRA, S.: Ordering MAD families a la Katětov,J. Symb. Log. 68 (2003), no. 4, 1337–1353.
  18. JALALI-NAINI, S.-A.: The Monotone Subsets of Cantor Space, Filters and Descriptive Set Theory: Ph.D. Thesis, University of Oxford, 1976.
  19. LACZKOVICH, M.—RECƁAW, I.: Ideal limits of sequences of continuous functions, Fundam. Math. 203 (2009), no. 1, 39–46.
  20. LAFLAMME, C.: Filter games and combinatorial properties of winning strategies, Contemp. Math. 192 (1995), 51–67.
  21. MAČAJ, M.—SLEZIAK, M.: ℐ𝒩-convergence, Real Anal. Exchange 36 (2010/11), no. 1, 177–193.
  22. MARTON, A.—ƠUPINA, J.: On P -like ideals induced by disjoint families,J.Math. Anal. Appl. 528 (2023), no. 2, Paper no. 127551.
  23. MEZA ALCÁNTARA, D.: Ideals and filters on countable sets: Ph. D. Thesis, Universidad Nacional Autonoma de Mexico, Mexico, 2009.
  24. REPICKÝ, M.: Cardinal invariants and the collapse of the continuum by Sacks forcing, J. Symb. Log. 73 (2008), no. 2, 711–727.
  25. STANISZEWSKI, M.: On ideal equal convergence II,J.Math. Anal.Appl. 451 (2017), no. 2, 1179–1197.
  26. SZEMERÉDI, E.: On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), no. 1, 199–245.
  27. ƠUPINA, J.: Ideal QN-spaces, J. Math. Anal. Appl. 435 (2016), no. 1, 477–491.
  28. TALAGRAND, M.: Compacts de fonctions mesurables et filtres non mesurables,Acta Arith. 67 (1980), no. 1, 13–43.
DOI: https://doi.org/10.2478/tmmp-2023-0025 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 73 - 88
Submitted on: Nov 10, 2022
Published on: Nov 16, 2023
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2023 Adam Marton, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.