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Splitting number at uncountable cardinals

Published online by Cambridge University Press:  12 March 2014

Jindřich Zapletal
Jindřich Zapletal*
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA, E-mail: [email protected]
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Abstract

We study a generalization of the splitting number s to uncountable cardinals. We prove that 𝔰(κ) > κ+ for a regular uncountable cardinal κ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption 𝔰(ℵω) > ℵω+1 has a considerable large cardinal strength as well.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 35 - 42
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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