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Applications of ρ-Functions

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Set Theory

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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?

The exponential function. This is undoubtedly the most important function in mathematics.

Walter Rudin; Prologue to Real and Complex Analysis

The author was partially supported by the NSF Grant DMS-9505098. The author was also partially supported during the conference by Centre de Recerca Matemàtica (CRM) for which he is very grateful to the organizers of the conference: Joan Bagaria and Adrian Mathias.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Auburn University, Auburn, AL, 36849-5319, USA

    Piotr Koszmider

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  1. Piotr Koszmider
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Editor information

Editors and Affiliations

  1. Instituto Venezolano de Investigaciones Cientificas, Caracas, Venezuela

    Carlos Augusto Di Prisco

  2. University of Florida, Gainesville, Florida, USA

    Jean A. Larson

  3. Universitat de Barcelona, Barcelona, Spain

    Joan Bagaria

  4. University of Wales, Aberystwyth, Wales, UK

    A. R. D. Mathias

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© 1998 Springer Science+Business Media Dordrecht

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Koszmider, P. (1998). Applications of ρ-Functions. In: Di Prisco, C.A., Larson, J.A., Bagaria, J., Mathias, A.R.D. (eds) Set Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8988-8_6

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  • DOI: https://doi.org/10.1007/978-94-015-8988-8_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4978-0

  • Online ISBN: 978-94-015-8988-8

  • eBook Packages: Springer Book Archive

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