Cofinality of normal ideals on Pκ(λ) II

Pierre Matet; Cédric Péan; Saharon Shelah

doi:10.1007/BF02762383

Cofinality of normal ideals on Pκ(λ) II

Pierre Matet^*
, Cédric Péan
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Review article › peer-review

9 Scopus citations

Abstract

For an ideal J on an infinite set X with add(J) = κ, let cof̄(J) be the smallest size of any subfamily Y of J with the property that any member of J can be covered by less than κ members of Y. We study the value of cof̄(NS_κ,λ^[δ]<θ| A) for A in (NS_κ,λ^[δ]<θ)⁺, where NS_κ,λ^[δ]<θdenotes the smallest [δ]^<θ-normal ideal on P _κ(λ). We also discuss the problem of whether there exists a set A such that NS_κ,λ ^[δ]<θ = I_κ,λ | A, or even NS_κ,λ^[δ]<θ |A=I _κ,λ | A.

Original language	English
Pages (from-to)	253-283
Number of pages	31
Journal	Israel Journal of Mathematics
Volume	150
DOIs	https://doi.org/10.1007/BF02762383
State	Published - 2005

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title = "Cofinality of normal ideals on Pκ(λ) II",

abstract = "For an ideal J on an infinite set X with add(J) = κ, let co{\=f}(J) be the smallest size of any subfamily Y of J with the property that any member of J can be covered by less than κ members of Y. We study the value of co{\=f}(NSκ,λ[δ]<θ| A) for A in (NSκ,λ[δ]<θ)+, where NSκ,λ[δ]<θdenotes the smallest [δ]<θ-normal ideal on P κ(λ). We also discuss the problem of whether there exists a set A such that NSκ,λ [δ]<θ = Iκ,λ | A, or even NSκ,λ[δ]<θ |A=I κ,λ | A.",

author = "Pierre Matet and C{\'e}dric P{\'e}an and Saharon Shelah",

year = "2005",

doi = "10.1007/BF02762383",

language = "אנגלית",

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AU - Matet, Pierre

AU - Péan, Cédric

AU - Shelah, Saharon

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N2 - For an ideal J on an infinite set X with add(J) = κ, let cof̄(J) be the smallest size of any subfamily Y of J with the property that any member of J can be covered by less than κ members of Y. We study the value of cof̄(NSκ,λ[δ]<θ| A) for A in (NSκ,λ[δ]<θ)+, where NSκ,λ[δ]<θdenotes the smallest [δ]<θ-normal ideal on P κ(λ). We also discuss the problem of whether there exists a set A such that NSκ,λ [δ]<θ = Iκ,λ | A, or even NSκ,λ[δ]<θ |A=I κ,λ | A.

AB - For an ideal J on an infinite set X with add(J) = κ, let cof̄(J) be the smallest size of any subfamily Y of J with the property that any member of J can be covered by less than κ members of Y. We study the value of cof̄(NSκ,λ[δ]<θ| A) for A in (NSκ,λ[δ]<θ)+, where NSκ,λ[δ]<θdenotes the smallest [δ]<θ-normal ideal on P κ(λ). We also discuss the problem of whether there exists a set A such that NSκ,λ [δ]<θ = Iκ,λ | A, or even NSκ,λ[δ]<θ |A=I κ,λ | A.

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VL - 150

SP - 253

EP - 283

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Cofinality of normal ideals on Pκ(λ) II

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