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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

REFERENCES

Merimovich, Carmi, Extender based Magidor-Radin forcing. Israel Journal of Mathematics, vol. 182 (2011), pp. 439–480.CrossRefGoogle Scholar
Zapletal, Jindřich, Splitting number at uncountable cardinals, this Journal, vol. 62 (1997), pp. 35–42.Google Scholar
Suzuki, Toshio, About splitting numbers. Proceedings of the Japan Academy Series A Mathematical Sciences, vol. 74 (1998), no. 2, pp. 33–35.CrossRefGoogle Scholar
Gitik, Moti, The strenght of the failure of the singular cardinal hypothesis. Annals of Pure and Applied Logic, vol. 51 (1991), no. 3, pp. 215–240.CrossRefGoogle Scholar
Gitik, Moti, Prikry type forcings, Handbook of set theory (Foreman, Kanamori, editors), vol. 2, chap. 16, pp. 1351–1448.CrossRefGoogle Scholar
Gitik, Moti, On measurable cardinals violating the continuum hypothesis. Annuals of Pure and Applied Logic, vol. 63 (1993), pp. 227–240.CrossRefGoogle Scholar
Gitik, M., Kanovei, V., and Koepke, P., Intermediate models of Prikry generic extensions, http://www.math.tau.ac.il/∼gitik.Google Scholar
Shelah, Saharon, Further Cardinal Arithmetic. Israel Journal Of Mathematics, vol. 95 (1996), pp. 61–114.CrossRefGoogle Scholar
Shelah, Saharon, Cardinal Arithmetic, Oxford University Press, Oxford, 1994.CrossRefGoogle Scholar
Shelah, Saharon, Inner Models and Large Cardinals, de Gruyter, Berlin, 2001.Google Scholar