Q-pointness, P-pointness and feebleness of ideals

Matet, Pierre; Pawlikowski, Janusz

doi:10.2178/jsl/1045861512

Cited by 2 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zapletal [21] investigated the splitting number s λ -here the situation is really complicated as the inequality s λ > λ + needs large cardinals. One of the sources of interest in characteristics of the λ-reals is their relevance for our understanding of the club filter on λ (or the dual ideal on non-stationary subsets of λ) -see, e.g., Balcar and Simon [2, §5], Landver [9], Matet and Pawlikowski [10], Matet, Ros lanowski and Shelah [11]. First steps toward developing forcing for λ-reals has been done long time ago: in 1980 Kanamori [8] presented a systematic treatment of the λ-perfect-set forcing in products and iterations.…”

Section: Introductionmentioning

confidence: 99%

Sheva-sheva-sheva: Large creatures

Roslanowski

Shelah

2007

Isr. J. Math.

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Sheva-sheva-sheva: Large creatures

Roslanowski

Shelah

2007

Isr. J. Math.

View full text Add to dashboard Cite

“…If there is a family of size κ +ω of pairwise almost disjoint cofinal subsets of κ, then there is a κ-complete ideal J on κ such that cof(J ) < cof(J ) (see Matet and Pawlikowski [9]). …”

Section: Lemma 14 Let µ Be a Regular Infinite Cardinal Then U(µ µmentioning

confidence: 99%

Cofinality of the nonstationary ideal

Matet¹,

Roslanowski

Shelah

2005

Trans. Amer. Math. Soc.

Self Cite

View full text Add to dashboard Cite

Abstract. We show that the reduced cofinality of the nonstationary ideal NS κ on a regular uncountable cardinal κ may be less than its cofinality, where the reduced cofinality of NS κ is the least cardinality of any family F of nonstationary subsets of κ such that every nonstationary subset of κ can be covered by less than κ many members of F . For this we investigate connections of the various cofinalities of NS κ with other cardinal characteristics of κ κ and we also give a property of forcing notions (called manageability) which is preserved in <κ-support iterations and which implies that the forcing notion preserves non-meagerness of subsets of κ κ (and does not collapse cardinals nor changes cofinalities). IntroductionLet κ be a regular uncountable cardinal. For C ⊆ κ and γ ≤ κ, we say that γ is a limit point of C if (C ∩ γ) = γ > 0. C is closed unbounded if C is a cofinal subset of κ containing all its limit points less than κ. A set A ⊆ κ is nonstationary if A is disjoint from some closed unbounded subset C of κ. The nonstationary subsets of κ form an ideal on κ denoted by NS κ . The cofinality of this ideal, cof(NS κ ), is the least cardinality of a family F of nonstationary subsets of κ such that every nonstationary subset of κ is contained in a member of F. The reduced cofinality of NS κ , cof(NS κ ), is the least cardinality of a family F ⊆ NS κ such that every nonstationary subset of κ can be covered by less than κ many members of F. This paper addresses the question of whether cof(NS κ ) = cof(NS κ ). Note thatso under GCH we have cof(NS κ ) = cof(NS κ ). Let κ 2 be endowed with the κ-box product topology, 2 itself considered discrete. We say that a set W ⊆ κ 2 is κ-meager if there is a sequence U α : α < κ of dense open subsets of κ 2 such that W ∩ α<κ U α = ∅. The covering number for the category of the space κ 2, denoted cov(M κ,κ ), is the least cardinality of any collection X of

show abstract

Q-pointness, P-pointness and feebleness of ideals

Abstract: We study the degree of (weak) (Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.

Cited by 2 publications

References 16 publications

Sheva-sheva-sheva: Large creatures

Sheva-sheva-sheva: Large creatures

Cofinality of the nonstationary ideal

Contact Info

Product

Resources

About