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Applications of ρ-Functions

In: Set Theory

Author

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  • Piotr Koszmider

    (Auburn University, Department of Mathematics)

Abstract

Once we start measuring mathematical objects using infinite cardinals we are led naturally into two-cardinal combinatorics which is a field about combinatorial constructions with associated two cardinals. Various internal and external questions can be asked, all related to the relation between the two associated cardinals, e.g.: What could be heights of superatomic Boolean algebras with countable width? What are the possible sizes of Hausdorff spaces with points Gδ and countable Lindelof degree? Is it possible to construct a c.c.c forcing notion (and in particular a cardinal preserving forcing notion) that adds a function f: ω2 × ω2 → ω which isn’t constant on a product of any two infinite sets?

Suggested Citation

  • Piotr Koszmider, 1998. "Applications of ρ-Functions," Springer Books, in: Carlos Augusto Di Prisco & Jean A. Larson & Joan Bagaria & A. R. D. Mathias (ed.), Set Theory, pages 83-98, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-8988-8_6
    DOI: 10.1007/978-94-015-8988-8_6
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