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Cardinal invariants associated with Fubini product of ideals

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Abstract

We prove some results displaying the relationship between Fubini product of ideals and its factor ideals, and study a partial order using the cardinal invariant of the continuum. The relationships among transitive cardinal invariants of abelian group are also investigated.

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References

  1. Balcar B, Hernández-Hernández F, Hrušák M. Combinatories of dense subsets of the rationals. Fund Math, 2004, 183: 59–80

    Article  MATH  MathSciNet  Google Scholar 

  2. Balcar B, Simon P. Disjoint refinement. In: Monk J D, Bonnet R, eds. Handbook of Boolean Algebra, Vol. 2. Amsterdam: North-Holland, 1989, 333–386

    Google Scholar 

  3. Bartoszyánski T, Judah H. Set Theory on the Structure of the Real Line. Wellesley: A K Peters, 1995

    Google Scholar 

  4. Blass A. Combinatorial cardinal characteristics of the continuum. In: Kanamori A, et al., eds. Handbook of Set Theory. London: Springer, 2010

    Google Scholar 

  5. Brendle J. Van Douwens diagram for dense sets of rationals, Ann Pure Appl Logic, 2006, 143: 54–69

    Article  MATH  MathSciNet  Google Scholar 

  6. Brendle J. Distinguishing groupwise density numbers. Monatsh Math, 2007, 152: 207–215

    Article  MATH  MathSciNet  Google Scholar 

  7. Cichoán J. On dense subsets of rational numbers. Acta Univ Carolin Math Phys, 2001, 42: 5–10

    MathSciNet  Google Scholar 

  8. Keremedis K. On the covering and the additivity number of the real line. Proc Amer Math Soc, 1995, 123: 1583–1590

    Article  MATH  MathSciNet  Google Scholar 

  9. Kraszewski J. Transitive properties of the ideal \( \mathbb{S}_2 \). Real Anal Exchange, 2003/2004, 20: 629–638

    MathSciNet  Google Scholar 

  10. Matet P, Pawlikowski J. Ideals over ω and cardinal invariants of the continuum. J Symbolic Logic, 1998, 63: 1040–1054

    Article  MATH  MathSciNet  Google Scholar 

  11. Roslanowski A. On game ideals. Colloq Math, 1990, LIX: 159–168

    MathSciNet  Google Scholar 

  12. Stepräns J. The almost disjointness cardinal invariant in the quotient algebra of the rationals modulo the nowhere dense subsets. Real Anal Exchange, 2001/2002, 27: 795–800

    MathSciNet  Google Scholar 

  13. Van Douwen E K. The integers and topology. In: Kunen K, Vaughhan J E, eds. Handbook of Set-Theoretic Topology. Amsterdam: North-Holland, 1984, 111–167

    Google Scholar 

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  1. College of Mathematics, Sichuan University, Chengdu, 610064, China

    JianYong Hong & ShuGuo Zhang

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  1. JianYong Hong
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  2. ShuGuo Zhang
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Correspondence to ShuGuo Zhang.

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Hong, J., Zhang, S. Cardinal invariants associated with Fubini product of ideals. Sci. China Math. 53, 425–430 (2010). https://doi.org/10.1007/s11425-009-0144-1

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  • DOI: https://doi.org/10.1007/s11425-009-0144-1

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