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Bounded Martin’s Maximum and Strong Cardinals

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Set Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

We show that if Bounded Martin’s Maximum (BMM) holds then for every X ∈ V there is an inner model with a strong cardinal containing X. We also discuss various open questions which are related to BMM.

The main result of this note was proven in February 2004 while the author was a guest at the CRM in Barcelona. He would like to thank Neus Portet and Joan Bagaria for their warm hospitality.

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References

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Author information

Authors and Affiliations

  1. Institut für Mathematische Logik und Grundlagenforschung, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149, Münster, Germany

    Ralf Schindler

Authors
  1. Ralf Schindler
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Editor information

Editors and Affiliations

  1. Departament de Lògica, Història I Filosofia de la Ciència, Universitat de Barcelona, Baldiri Reixac s/n, 08028, Barcelona, Spain

    Joan Bagaria

  2. Department of Mathematics, University of Toronto, Toronto, M5S 2E4, Canada

    Stevo Todorcevic

  3. C.N.R.S., UMR 7056, Université Paris 7, 2, Place Jussieu Case 7012, 75251, Paris Cedex 05, France

    Stevo Todorcevic

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Schindler, R. (2006). Bounded Martin’s Maximum and Strong Cardinals. In: Bagaria, J., Todorcevic, S. (eds) Set Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7692-9_15

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