Switch to: References

Add citations

You must login to add citations.
  1. Ideal convergence of bounded sequences.Rafał Filipów, Recław Ireneusz, Mrożek Nikodem & Szuca Piotr - 2007 - Journal of Symbolic Logic 72 (2):501-512.
    We generalize the Bolzano-Weierstrass theorem on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • Continuum-Many Boolean Algebras of the Form [image] Borel.Michael Ray Oliver - 2004 - Journal of Symbolic Logic 69 (3):799 - 816.
    We examine the question of how many Boolean algebras, distinct up to isomorphism, that are quotients of the powerset of the naturals by Borel ideals, can be proved to exist in ZFC alone. The maximum possible value is easily seen to be the cardinality of the continuum $2^{\aleph_{0}}$ ; earlier work by Ilijas Farah had shown that this was the value in models of Martin's Maximum or some similar forcing axiom, but it was open whether there could be fewer in (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Four and more.Ilijas Farah & Jindřich Zapletal - 2006 - Annals of Pure and Applied Logic 140 (1):3-39.
    We isolate several large classes of definable proper forcings and show how they include many partial orderings used in practice.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations