An ideal characterization of mahlo cardinals

Journal of Symbolic Logic 54 (2):467-473 (1989)
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 $\lambda^{ then there is a nontrivial κ-complete κ-normal fine ideal on P κ (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) $\mu^{ if and only if there is a nontrivial κ-complete weakly κ-normal ideal on κ, and (2) if $\mu^{ then there is a nontrivial κ-complete weakly κ-normal fine ideal on P κ (λ)
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DOI 10.2307/2274861
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Some Combinatorial Problems Concerning Uncountable Cardinals.Thomas J. Jech - 1973 - Annals of Mathematical Logic 5 (3):165-198.

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