On the space (λ)κ

We study normal filters on the set spaces λ , P κ ( λ ) , [ λ ] κ \lambda ,{\mathcal {P}_\kappa }\left ( \lambda \right ),{\left [ \lambda \right ]^\kappa } , and ( λ ) κ {\left ( \lambda \right )^\kappa } . We characterize the least normal γ \gamma -complete filter containing a given γ \gamma -complete filter for γ ≥ ω 1 \gamma \geq {\omega _1} . If F \mathcal {F} is a ω 1 {\omega _1} -complete filter on any of the set spaces mentioned, the least ω 1 {\omega _1} -complete normal filter containing it is the filter generated by the sets { x ∈ E | α 1 , … , α n ∈ x → x ∈ f ( α 1 , … , α n ) } \left \{ {x \in E\left | {{\alpha _1}, \ldots ,{\alpha _n} \in x \to x \in f\left ( {{\alpha _1}, \ldots ,{\alpha _n}} \right )} \right .} \right \} where f : λ > ω → F f:{\lambda ^{ > \omega }} \to \mathcal {F} .

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On the space (λ)κ

Cited by 2 publications

References 3 publications

Filter spaces: towards a unified theory of large cardinal and embedding axioms

Filter spaces: towards a unified theory of large cardinal and embedding axioms

Normal filters generated by a family of sets

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