Archive for Mathematical Logic

, Volume 45, Issue 6, pp 705–714 | Cite as

Orders of Indescribable Sets

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Abstract

We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal.

Keywords

Weakly compact cardinal Weakly compact set Saturation of ideal Mahlo operation 

Mathematics Subject Classification (2000)

03E55 03E05 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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