Archive for Mathematical Logic

, Volume 56, Issue 7–8, pp 715–723 | Cite as

On the consistency strength of level by level inequivalence

  • Arthur W. ApterEmail author


We show that the theories “ZFC \(+\) There is a supercompact cardinal” and “ZFC \(+\) There is a supercompact cardinal \(+\) Level by level inequivalence between strong compactness and supercompactness holds” are equiconsistent.


Supercompact cardinal Strongly compact cardinal Level by level inequivalence between strong compactness and supercompactness Nonreflecting stationary set of ordinals Equiconsistency 

Mathematics Subject Classification

03E35 03E55 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsBaruch College of CUNYNew YorkUSA
  2. 2.Department of MathematicsThe CUNY Graduate CenterNew YorkUSA

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