Katětov order on Borel ideals

1. Arciga-Alejandre, M., Hrušák, M., Martinez-Ranero, C.: Invariance properties of almost disjoint families. J. Symb. Log. 78(3), 989–999 (2013)

   Article  MathSciNet  MATH  Google Scholar 

2. Bartoszyński, T., Judah, H.: Set Theory. On the Structure of the Real Line. A K Peters, Wellesley, MA (1995)

   MATH  Google Scholar 

3. Baumgartner, J.E.: Ultrafilters on \(\omega \). J. Symb. Log. 60(2), 624–639 (1995)

   Article  MATH  Google Scholar 

4. Brendle, J., Flašková, J.: Generic existence of ultrafilters on the natural numbers. Fund. Math. 236(3), 201–245 (2017)

   Article  MathSciNet  MATH  Google Scholar 

5. Brendle, J., Hrušák, M.: Countable Fréchet Boolean groups: an independence result. J. Symb. Log. 74(3), 1061–1068 (2009)

   Article  MATH  Google Scholar 

6. Brendle, J., Yatabe, S.: Forcing indestructibility of MAD families. Ann. Pure Appl. Logic 132(2–3), 271–312 (2005)

   Article  MathSciNet  MATH  Google Scholar 

7. Christensen, J.P.R.: Some results with relation to the control measure problem. In: Vector Space Measures and Applications (Proceedings Conference, University of Dublin, Dublin, 1977), II, volume 77 of Lecture Notes in Physics, pp. 27–34. Springer, Berlin (1978)

8. Daguenet, M.: Emploi des filtres sur n dans l’étude descriptive des fonctions. Fundam. Math. 95, 11–33 (1977)

   MathSciNet  MATH  Google Scholar 

9. Ilijas, F.: 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 

10. Flašková, J.: Description of some ultrafilters via I-ultrafilters. In: Proceedings of RIMS, vol. 1619 (2008)

11. Hrušák, M.: MAD families and the rationals. Comment. Math. Univ. Carol. 42(2), 345–352 (2001)

    MathSciNet  MATH  Google Scholar 

12. Hrušák, M.: Combinatorics of filters and ideals. In: Set Theory and Its Applications, volume 533 of Contemporary Mathematics, pp. 29–69. American Mathematical Society, Providence, RI (2011)

13. Hrušák, M., Ferreira, S.G.: Ordering MAD families a la Katětov. J. Symb. Log. 68(4), 1337–1353 (2003)

    Article  MATH  Google Scholar 

14. Hrušák, M., Meza-Alcántara, D.: Katětov order, Fubini property and Hausdorff ultrafilters. Rend. Istit. Mat. Univ. Trieste 44, 503–511 (2012)

    MathSciNet  MATH  Google Scholar 

15. Hrušák, M., Minami, H.: Mathias–Prikry and Laver–Prikry type forcing. Ann. Pure Appl. Logic 165(3), 880–894 (2014)

    Article  MathSciNet  MATH  Google Scholar 

16. Hrušák, M., Zapletal, J.: Forcing with quotients. Arch. Math. Log. 47(7–8), 719–739 (2008)

    MathSciNet  MATH  Google Scholar 

17. Hrušák, M., Ramos García, U.A.: Malykhin’s problem. Adv. Math. (2014)

18. Hrušák, M., Meza-Alcántara, D., Minami, H.: Pair-splitting, pair-reaping and cardinal invariants of \({F}_\sigma \) ideals. J. Symb. Log. 75(2), 661–677 (2010)

    Article  MathSciNet  MATH  Google Scholar 

19. Hrušák, M., Meza-Alcántara, D., Thümmel, E., Uzcategui, C.: Ramsey type properties of ideals. Accepted to Annals of Pure and Applied Logic (2017)

20. Kanovei, V., Reeken, M.: New Radon–Nikodym ideals. Mathematika 47(1–2), 219–227 (2002)

    MathSciNet  MATH  Google Scholar 

21. Katětov, M.: Products of filters. Comment. Math. Univ. Carol. 9, 173–189 (1968)

    MathSciNet  MATH  Google Scholar 

22. Kechris, A.S.: Classical Descriptive Set Theory, volume 156 of Graduate Texts in Mathematics. Springer, New York (1995)

    Book  Google Scholar 

23. Kelley, J.L.: Measures on Boolean algebras. Pac. J. Math. 9, 1165–1177 (1959)

    Article  MathSciNet  MATH  Google Scholar 

24. Laczkovich, M., Recław, I.: Ideal limits of sequences of continuous functions. Fundam. Math. 203(1), 39–46 (2009)

    Article  MathSciNet  MATH  Google Scholar 

25. Laflamme, C.: Zapping small filters. Proc. Am. Math. Soc. 114(2), 535–544 (1992)

    Article  MathSciNet  MATH  Google Scholar 

26. Laflamme, C.: Filter games and combinatorial properties of strategies. In: Set Theory (Boise, ID, 1992–1994), volume 192 of Contemporary Mathematics, pp. 51–67. American Mathematical Society, Providence, RI (1996)

27. Mazur, K.: \({F}_{\sigma }\)-ideals and \(\omega _{1}\omega _{1}^{*}\)-gaps in the boolean algebras \({\cal{P}}(\omega )/{I}\). Fundam. Math. 138(2), 103–111 (1991)

    MathSciNet  Google Scholar 

28. Meza Alcántara, D: Ideals and Filters on Countable Sets. PhD thesis, UNAM México, (2009)

29. Solecki, S.: Analytic ideals. Bull. Symb. Log. 2(3), 339–348 (1996)

    Article  MathSciNet  MATH  Google Scholar 

30. Solecki, S.: Analytic ideals and their applications. Ann. Pure Appl. Log. 99(1–3), 51–72 (1999)

    Article  MathSciNet  MATH  Google Scholar 

31. Solecki, S.: Filters and sequences. Fundam. Math. 163(3), 215–228 (2000)

    MathSciNet  MATH  Google Scholar 

Download references