A long chain of P-points

Kuzeljević, Boriša; Raghavan, Dilip

doi:10.1142/s0219061318500046

Cited by 7 publications

(16 citation statements)

References 10 publications

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“…[15], [9], [13]). The results that motivated the research that went into this paper were obtained by B. Kuzeljević and D. Raghavan [7]. They showed Theorem (Kuzeljević and Raghavan).…”

Section: Introductionmentioning

confidence: 77%

Chains of P-points

Raghavan¹,

Verner²

2019

Can. Math. Bull.

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It is proved that the Continuum Hypothesis implies that any sequence of rapid P-points of length < c + which is increasing with respect to the Rudin-Keisler ordering is bounded above by a rapid P-point. This is an improvement of a result from [7]. It is also proved that Jensen's diamond principle implies the existence of an unbounded strictly increasing sequence of P-points of length ω 1 in the Rudin-Keisler ordering. This shows that restricting to the class of rapid P-points is essential for the first result. c + -closed:Theorem. Assume CH. Any increasing sequence of rapid P-points of length < c + is bounded above by a rapid P-point.2010 Mathematics Subject Classification. Primary 03E50, 03E05, 54D80.

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“…[15], [9], [13]). The results that motivated the research that went into this paper were obtained by B. Kuzeljević and D. Raghavan [7]. They showed Theorem (Kuzeljević and Raghavan).…”

Section: Introductionmentioning

confidence: 77%

Chains of P-points

Raghavan¹,

Verner²

2019

Can. Math. Bull.

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“…By K önig Lemma if all branches are finite, then the height of the tree T is finite, and so there are irremovable finite sets in contrary to (6). Thus there is infinite branch and the whole set j≤i h -1 i (P) ∩ W l is removable.…”

Section: Theorem 312 (B = C) There Exists An Order-embedding Of the Real Line Into The Set Of P-pointsmentioning

confidence: 98%

“…In [1], A. Blass asked (Question 4) which ordinals could be embedded in the set of P-points, noticing that such an ordinal could not be greater than c + . The question was also considered by D. Raghavan and S. Shelah in [8] and answered, under MA, by B. Kuzeljević and D. Raghavan in a recent paper [6].…”

Section: Fact 32 Let a Be A Centered Family Of Subsets Of Such That A ∪ {F } Is Not An Ultrafilter Subbase For Any F Compatible With A Lementioning

confidence: 99%

“…An inspection of our proofs indicates a possibility of refinement of most results with the aid of an, a priori, new cardinal invariant. We define q to be the minimal cardinality of families B, for which there exists a family A such that A ∪ B includes a contour, and A ∪ C includes no contour for every countable family C. 6 If P is a collection of families such that P ∈ P whenever P includes a contour, then q fulfills q = min {card (B) :…”

Section: Theorem 312 (B = C) There Exists An Order-embedding Of the Real Line Into The Set Of P-pointsmentioning

confidence: 99%

“…We show that under b = c each ordinal less than c + is order-embeddable into P-points. A recent paper by B. Kuzeljević and D. Raghavan [6] answers the question of the embedding of ordinals into P-points under MA. §2.…”

mentioning

confidence: 99%

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THE RUDIN–KEISLER ORDERING OF P-POINTS UNDER 𝔟 = 𝔠

Starosolski¹

2021

J. symb. log.

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M. E. Rudin (1971) proved, under CH, that for each P-point p there exists a P-point q strictly RK-greater than p. This result was proved under ${\mathfrak {p}= \mathfrak {c}}$ by A. Blass (1973), who also showed that each RK-increasing $ \omega $ -sequence of P-points is upper bounded by a P-point, and that there is an order embedding of the real line into the class of P-points with respect to the RK-ordering. In this paper, the results cited above are proved under the (weaker) assumption that $\mathfrak { b}=\mathfrak {c}$ . A. Blass asked in 1973 which ordinals can be embedded in the set of P-points, and pointed out that such an ordinal cannot be greater than $ \mathfrak {c}^{+}$ . In this paper it is proved, under $\mathfrak {b}=\mathfrak {c}$ , that for each ordinal $\alpha < \mathfrak {c}^{+}$ , there is an order embedding of $ \alpha $ into P-points. It is also proved, under $\mathfrak {b}=\mathfrak {c}$ , that there is an embedding of the long line into P-points.

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Cofinal types on ω₂

Kuzeljević

Todorčević

2023

Mathematical Logic Qtrly

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In this paper we start the analysis of the class scriptDℵ2$\mathcal {D}_{\aleph _2}$, the class of cofinal types of directed sets of cofinality at most ℵ2. We compare elements of scriptDℵ2$\mathcal {D}_{\aleph _2}$ using the notion of Tukey reducibility. We isolate some simple cofinal types in scriptDℵ2$\mathcal {D}_{\aleph _2}$, and then proceed to find some of these types which have an immediate successor in the Tukey ordering of scriptDℵ2$\mathcal {D}_{\aleph _2}$.

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A long chain of P-points

Cited by 7 publications

References 10 publications

Chains of P-points

Chains of P-points

THE RUDIN–KEISLER ORDERING OF P-POINTS UNDER 𝔟 = 𝔠

Cofinal types on ω₂

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A long chain of P-points

Cited by 7 publications

References 10 publications

Chains of P-points

Chains of P-points

THE RUDIN–KEISLER ORDERING OF P-POINTS UNDER 𝔟 = 𝔠

Cofinal types on ω2

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Cofinal types on ω₂