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Reflection and indescribability in the constructible universe

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Abstract

We extend a result of R. Jensen ([6]) by showing that in the constructible universe, a regular cardinal is (n + 1)-stationary if and only if it is Π 1 n -indescribable.

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References

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Author information

Authors and Affiliations

  1. ICREA (Institució Catalana de Recerca i Estudis Avançats) and Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001, Barcelona, Catalonia, Spain

    Joan Bagaria

  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904, Israel

    Menachem Magidor

  3. Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501, Japan

    Hiroshi Sakai

Authors
  1. Joan Bagaria
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  2. Menachem Magidor
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  3. Hiroshi Sakai
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Corresponding author

Correspondence to Joan Bagaria.

Additional information

The research work of the first author was partially supported by the Spanish Ministry of Science and Innovation under grant MTM2011-25229, and by the Generalitat de Catalunya (Catalan Government) under grant 2009 SGR 187. Part of this work was carried out while the first author was visiting the Albert Einstein Institute of Mathematics at The Hebrew University, Jerusalem, whose hospitality is gratefully acknowledged.

The research of the second author was supported by the Israel Science Foundation grant 817/11.

The third author was supported by JSPS KAKENHI Grant Number 23740076.

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Bagaria, J., Magidor, M. & Sakai, H. Reflection and indescribability in the constructible universe. Isr. J. Math. 208, 1–11 (2015). https://doi.org/10.1007/s11856-015-1191-7

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  • DOI: https://doi.org/10.1007/s11856-015-1191-7

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