On successors of singular cardinals

Saharon Shelah

doi:10.1016/S0049-237X(08)71635-5

On successors of singular cardinals

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

86 Scopus citations

Abstract

This chapter discusses the successors of singular cardinals and explains the situation for the successor of a strong limit singular cardinal λ. The chapter finds a special subset S* (λ⁺), from which the stationary subsets of λ⁺ can be found, which can be stopped from being stationary by μ-complete forcing. If λ is a singular strong limit, then for every normal two place function d from λ⁺ to κ = cfλ, S_o (d)≡ S_l (d) ∪ CF(λ⁺,≤ κ) ≡ λ⁺ - S* ( λ+) mod_Dλ+. Therefore, S_o (d) does not depend on d up to equivalence mod_Dλ+.

Original language	English
Pages (from-to)	357-380
Number of pages	24
Journal	Studies in Logic and the Foundations of Mathematics
Volume	97
Issue number	C
DOIs	https://doi.org/10.1016/S0049-237X(08)71635-5
State	Published - 1 Jan 1979

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On successors of singular cardinals

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