Archive for Mathematical Logic

, Volume 45, Issue 6, pp 705–714

Orders of Indescribable Sets


DOI: 10.1007/s00153-006-0015-1

Cite this article as:
Hellsten, A. Arch. Math. Logic (2006) 45: 705. doi:10.1007/s00153-006-0015-1


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.


Weakly compact cardinal Weakly compact set Saturation of ideal Mahlo operation 

Mathematics Subject Classification (2000)

03E55 03E05 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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