On the Singular Cardinal Hypothesis

1992/04/06 by William J. Mitchell, Mitchell, William J.
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.math/9204202

openalex publication_date 1992/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the core model for sequences of measures to prove a new lower bound for the consistency strength of the failure of the SCH: THEOREM (i) If there is a singular strong limit cardinal κ such that 2^κ> kappa⁺ then there is an inner model with a cardinal κ such that for all ordinals α α. (ii) If there is a singular strong limit cardinal κ of uncountable cofinality such that 2^κ> κ⁺ then there is an inner model with o(κ) = κ⁺⁺. Since this paper was originally submitted, Gitik has improved this result to give exact lower bounds.

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