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ON THE SPLITTING NUMBER AT REGULAR CARDINALS

Published online by Cambridge University Press:  22 December 2015

OMER BEN-NERIA  and
MOTI GITIK
OMER BEN-NERIA
Affiliation:
DEPARTMENT OF MATHEMATICS TEL AVIV UNIVERSITY TEL AVIV, ISRAELE-mail: omerbe3@post.tau.ac.il
MOTI GITIK
Affiliation:
DEPARTMENT OF MATHEMATICS TEL AVIV UNIVERSITY TEL AVIV, ISRAELE-mail: gitik@post.tau.ac.il
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Abstract

Let κ, λ be regular uncountable cardinals such that λ > κ+ is not a successor of a singular cardinal of low cofinality. We construct a generic extension with s(κ) = λ starting from a ground model in which o(κ) = λ and prove that assuming ¬0, s(κ) = λ implies that o(κ) ≥ λ in the core model.

Keywords

Cardinal invariantssplitting numberlarge cardinalsMitchell orderforcinginner models

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 4 , December 2015 , pp. 1348 - 1360
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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