A Note on Special Subsets of the Rudin-Frolík Order for Regulars
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Joanna Jureczko
ABSTRACT
We show that there is a set of 22 κ ultrafilters incomparable in the Rudin-Frolík order of βκ\κ, where κ is regular, for which no subset with more than one element has an infimum.
Acknowledgement
The author is very grateful to the anonymous reviewers for their insight in reading the previous version of this paper. Their remarks undoubtedly avoided many inaccuracies and made the text more readable.
REFERENCES
[1] BAKER, J.—KUNEN, K.: Limits in the uniform ultrafilters, Trans. Amer. Math. Soc. 353(10) (2001), 4083–4093.10.1090/S0002-9947-01-02843-4Suche in Google Scholar
[2] BOOTH, D.: Ultrafilters on a countable set, Ann. Math. Log. 2(1) (1970-71), 1–24.10.1016/0003-4843(70)90005-7Suche in Google Scholar
[3] BUKOVSKÝ, L.—BUTKOVIČOVÁ, E.: Ultrafilter with
[4] BUTKOVIČOVÁ, E.: Ultrafilters without immediate predecessors in Rudin-Frolk order, Comment. Math. Univ. Carolin. 23(4) (1982), 757–766.Suche in Google Scholar
[5] BUTKOVIČOVÁ, E.: Long chains in Rudin-Frolík order, Comment. Math. Univ. Carolin. 24(3) (1983), 563–570.Suche in Google Scholar
[6] BUTKOVIČOVÁ, E.: Subsets of
[7] BUTKOVIČOVÁ, E.: Decrasing chains without lower bounds in the Rudin-Frolík order, roc. Amer. Math. Soc. 109(1) (1990), 251–259.10.1090/S0002-9939-1990-1007490-8Suche in Google Scholar
[8] COMFORT, W. W.—NEGREPONTIS, S.: The Theory of Ultrafilters. Grundlehren Math. Wiss. 211, Springer-Verlag, New York-Heidelberg, 1974.10.1007/978-3-642-65780-1Suche in Google Scholar
[9] FROLÍK, Z.: Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87–91.10.1090/S0002-9904-1967-11653-7Suche in Google Scholar
[10] GITIK, M.: Some constructions of ultrafilters over a measurable cardinal, Ann. Pure Appl. Logic 171(8) (2020), Art. ID 102821.10.1016/j.apal.2020.102821Suche in Google Scholar
[11] JECH, T.: Set Theory. The Third Millennium Edition, revised and expanded, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Suche in Google Scholar
[12] JURECZKO, J.: Chains in the Rudin-Frolík order for regulars, https://arxiv.org/pdf/2304.0097.pdf.Suche in Google Scholar
[13] JURECZKO, J.: Decreasing chains without lower bounds in the Rudin-Frolík order for regulars, https://arxiv.org/pdf/2304.01398.pdf.Suche in Google Scholar
[14] JURECZKO, J.: Ultrafilters without immediate predecessors in Rudin-Frolík order for regulars, Results Math. 77(6) (2022), Art. No. 230, 11 pp.10.1007/s00025-022-01762-wSuche in Google Scholar
[15] JURECZKO, J.: On some constructions of ultrafilters over a measurable cardinal, in preparation.Suche in Google Scholar
[16] KANAMORI, A.: Ultrafilters over a measurable cardinal, Ann. Math. Log. 11 (1976), 315–356.10.1016/0003-4843(76)90012-7Suche in Google Scholar
[17] KUNEN, K.: Weak P-points in ℕ*, Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978), pp. 741–749, Colloq. Math. Soc. János Bolyai 23, North-Holland, Amsterdam-New York, 1980.Suche in Google Scholar
[18] RUDIN, M. E.: Types of ultrafilters, Topology Seminar Wisconsin, 1965, Princeton Universiy Press, Princeton, 1966.10.1515/9781400882076-021Suche in Google Scholar
[19] RUDIN, M. E.: Partial orders on the types in
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Artikel in diesem Heft
- A Note on Special Subsets of the Rudin-Frolík Order for Regulars
- The 2-Class Group of Certain Families of Imaginary Triquadratic Fields
- The Deranged Bell Numbers
- On Index and Monogenity of Certain Number Fields Defined by Trinomials
- The k-Generalized Lucas Numbers Close to a Power of 2
- Shifted Power of a Polynomial with Integral Roots
- Further Insights into the Mysteries of the Values of Zeta Functions at Integers
- Memoryless Properties on Time Scales
- A Study of the Higher-Order Schwarzian Derivatives of Hirotaka Tamanoi
- Besov and Triebel-Lizorkin Capacity in Metric Spaces
- Oscillation of Odd Order Linear Differential Equations with Deviating Arguments with Dominating Delay Part
- An Elliptic Type Inclusion Problem on the Heisenberg Lie Group
- Existence Result for a Double Phase Problem Involving the (p(x), q(x))-Laplacian Operator
- A New Series Space Derived by Absolute Generalized Nörlund Means
- Examples of Weinstein Domains in the Complement of Smoothed Total Toric Divisors
- The Uniform Effros Property and Local Homogeneity
- Limit Theorems for Weighted Sums of Asymptotically Negatively Associated Random Variables Under Some General Conditions
- The Unit-Gompertz Quantile Regression Model for the Bounded Responses
- An Extended Gamma-Lindley Model and Inference for the Prediction of Covid-19 in Tunisia
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