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Journal Articles Archive for Mathematical Logic Year : 2016

## Cofinality of normal ideals on [λ]<κ I

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Pierre Matet
• Function : Author
Cédric Péan
• Function : Author
Saharon Shelah
• Function : Author

#### Abstract

An ideal J on $$[\lambda ]^{<\kappa }$$ is said to be $$[\delta ]^{<\theta }$$-normal, where $$\delta$$ is an ordinal less than or equal to $$\lambda$$, and $$\theta$$ a cardinal less than or equal to $$\kappa$$, if given $$B_e \in J$$ for $$e \in [\delta ]^{<\theta }$$, the set of all $$a \in [\lambda ]^{<\kappa }$$ such that $$a \in B_e$$ for some $$e \in [a \cap \delta ]^{< \vert a \cap \theta \vert }$$ lies in J. We give necessary and sufficient conditions for the existence of such ideals and describe the smallest one, denoted by $$NS_{\kappa ,\lambda }^{[\delta ]^{<\theta }}$$. We compute the cofinality of $$NS_{\kappa ,\lambda }^{[\delta ]^{<\theta }}$$.

#### Domains

Mathematics [math] Logic [math.LO]

### Dates and versions

hal-02145582 , version 1 (03-06-2019)

### Identifiers

• HAL Id : hal-02145582 , version 1
• DOI :

### Cite

Pierre Matet, Cédric Péan, Saharon Shelah. Cofinality of normal ideals on [λ]<κ I. Archive for Mathematical Logic, 2016, 55 (5-6), pp.799-834. ⟨10.1007/s00153-016-0496-5⟩. ⟨hal-02145582⟩

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