P-Like Properties of Meager Ideals and Cardinal Invariants

[1] HAGA, K. B.—SCHRITTESSER, D.—TÖRNQUIST, A.: MAD families, determinacy, and forcing, J. Math. Log. 22 (2021), no. 1, 2150026. Search in Google Scholar

[2] BARTOSZYŃSKI, T.—JUDAH, H.: Set Theory: On the Structure of the Real Line. CRC Press (Taylor & Francis Group) London, 1995 Search in Google Scholar

[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. Search in Google Scholar

[4] BUKOVSKÁ, Z.: Thin sets in trigonometrical series and quasinormal convergence,Math. Slovaca 40 (1990), no. 1, 53–62. Search in Google Scholar

[5] Császár,Á.—Laczkovich, M. Discrete and equal convergence, Stud. Sci. Math. Hungar. 10 (1975), 463–472. Search in Google Scholar

[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. Search in Google Scholar

[7] FARKAS, B.—SOUKUP, L.: More on cardinal invariants of analytis P-ideals, Commentationes Mathematicae Universitatis Carolinae 50 (2009), no. 2, 281–295. Search in Google Scholar

[8] FARKAS, B.—ZDOMSKYY, L.: Ways of destruction, J. Symb. Log. 87 (2022), no. 3, 938–966. Search in Google Scholar

[9] FILIPÓW, R.—STANISZEWSKI, M.: On ideal equal convergence, Cent. Eur. J. Math. 12 (2014), no. 6, 896–910. Search in Google Scholar

[10] R. FILIPÓW, R.—STANISZEWSKI, M.: Pointwise versus equal (quasi-normal) convergence via ideals, J. Math. Anal. Appl. 422 (2015), no. 2, 995–1006. Search in Google Scholar

[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. Search in Google Scholar

[12] GUZMÁN-GONZÁLEZ, O.—HRUŠÁK, M.— MARTÍNEZ-RANERO, C. A.—RAMOS-GARÍA, U. A.: Generic existence of MAD families, J. Symb. Log. 82 (2017), no. 1, 303–316. Search in Google Scholar

[13] HALBEISEN, L.J.: Combinatorial Set Theory With a Gentle Introduction to Forcing. Springer-Verlag, Berlin, 2012. Search in Google Scholar

[14] HERNÁNDEZ-HERNÁNDEZ, F.—HRUŠÁK, M.: Cardinal invariants of analytic P-ideals, Canad. J. Math. 59 (2007), no. 3, 575–595. Search in Google Scholar

[15] HRUŠÁK, M.: Combinatorics of filters and ideals, Contemp. Math. 533 (2011), 29–69. Search in Google Scholar

[16] HRUŠÁK, M.: Katětov order on Borel ideals, Arch. Math. Logic 56 (2017), no. 3, 831–847. Search in Google Scholar

[17] HRUŠÁK, M.—GARĆIA-FERREIRA, S.: Ordering MAD families a la Katětov,J. Symb. Log. 68 (2003), no. 4, 1337–1353. Search in Google Scholar

[18] JALALI-NAINI, S.-A.: The Monotone Subsets of Cantor Space, Filters and Descriptive Set Theory: Ph.D. Thesis, University of Oxford, 1976. Search in Google Scholar

[19] LACZKOVICH, M.—RECŁAW, I.: Ideal limits of sequences of continuous functions, Fundam. Math. 203 (2009), no. 1, 39–46. Search in Google Scholar

[20] LAFLAMME, C.: Filter games and combinatorial properties of winning strategies, Contemp. Math. 192 (1995), 51–67. Search in Google Scholar

[21] MAČAJ, M.—SLEZIAK, M.: ℐ^𝒦-convergence, Real Anal. Exchange 36 (2010/11), no. 1, 177–193. Search in Google Scholar

[22] MARTON, A.—ŠUPINA, J.: On P -like ideals induced by disjoint families,J.Math. Anal. Appl. 528 (2023), no. 2, Paper no. 127551. Search in Google Scholar

[23] MEZA ALCÁNTARA, D.: Ideals and filters on countable sets: Ph. D. Thesis, Universidad Nacional Autonoma de Mexico, Mexico, 2009. Search in Google Scholar

[24] REPICKÝ, M.: Cardinal invariants and the collapse of the continuum by Sacks forcing, J. Symb. Log. 73 (2008), no. 2, 711–727. Search in Google Scholar

[25] STANISZEWSKI, M.: On ideal equal convergence II,J.Math. Anal.Appl. 451 (2017), no. 2, 1179–1197. Search in Google Scholar

[26] SZEMERÉDI, E.: On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), no. 1, 199–245. Search in Google Scholar

[27] ŠUPINA, J.: Ideal QN-spaces, J. Math. Anal. Appl. 435 (2016), no. 1, 477–491. Search in Google Scholar

[28] TALAGRAND, M.: Compacts de fonctions mesurables et filtres non mesurables,Acta Arith. 67 (1980), no. 1, 13–43. Search in Google Scholar