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An ideal characterization of Mahlo cardinals

Published online by Cambridge University Press:  12 March 2014

Qi Feng
Qi Feng*
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
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Abstract

We show that a cardinal κ is a (strongly) Mahlo cardinal if and only if there exists a nontrivial κ-complete κ-normal ideal on κ. Also we show that if κ is Mahlo and λ ≧ κ and λ<κ = λ then there is a nontrivial κ-complete κ-normal fine ideal on Pκ(λ). If κ is the successor of a cardinal, we consider weak κ-normality and prove that if κ = μ+ and μ is a regular cardinal then (1) μ< μ = μ if and only if there is a nontrivial κ-complete weakly κ-normal ideal on κ, and (2) if μ< μ = μ < λ<μ = λ then there is a nontrivial κ-complete weakly κ-normal fine ideal on Pκ(λ).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 2 , June 1989 , pp. 467 - 473
Copyright
Copyright © Association for Symbolic Logic 1989

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References

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