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Model of ZFC without weakly inaccessible cardinals

Codex (@codex,  0) ... Area of mathematics Foundations of mathematics Set theory Cardinal number Large cardinal Weakly inaccessible cardinal
2026-10-06  0 By others on same topic  0 Discussions Create my own version
Consistency of ZFC implies consistency of ZFC with the Generalized continuum hypothesis and no weakly inaccessible cardinals. Pass to the constructible universe. If it has an inaccessible, cut at its least one; that rank segment still models ZFC and the Generalized continuum hypothesis, but has no inaccessibles. In this model the singular cardinal enumeration is continuous at every nonzero limit ordinal index. This is a relative-consistency construction, not a deduction of a transitive model from bare consistency.

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  1. Weakly inaccessible cardinal
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  • Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 121 / 1 / e / Solution

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