Bulletin of the Iranian Mathematical Society

, Volume 44, Issue 5, pp 1117–1124 | Cite as

On Some Properties of Shelah Cardinals

  • Ali Sadegh Daghighi
  • Massoud Pourmahdian
Original Paper


We present several results concerning Shelah cardinals including the fact that small and fast function forcings preserve Shelah and \((^{\kappa }\kappa \cap V)\)-Shelah cardinals, respectively. Furthermore, we prove that the Laver Diamond Principle holds for Shelah cardinals and use this fact to show that Shelah cardinals can be made indestructible under \(\le \kappa \)-directed closed forcings of size \(<wt(\kappa )\).


Shelah cardinal Small forcing Fast function forcing Laver diamond principle 

Mathematics Subject Classification

Primary 03E55 Secondary 03E05 



The authors would like to thank Mohammad Golshani for careful reading of the primary draft and the anonymous referee for making useful comments which led to various improvements in the text. We also would like to especially thank the journal editor, Ali Enayat, for his sincere efforts during the communications between the authors and referee.


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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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