Chains in the Rudin-Frolík order
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Joanna Jureczko
Abstract
The aim of this paper is to construct chains of length (2κ)+ in the Rudin-Frolík order of β κ for every infinite κ.
Acknowledgement
The author is very grateful to the anonymous reviewer for their insight in reading the previous version of this paper. Their remarks undoubtedly avoided many inaccuracies and made the text more readable.
Communicated by L’ubica Holá
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. Logic 2(1) (1970/71), 1–24.10.1016/0003-4843(70)90005-7Suche in Google Scholar
[3] Bukovský, L.—Butkovičová, E.: Ultrafilters with ℵ0 predecessors in Rudin-Frolík order, Comment. Math. Univ. Carolin. 22(3) (1981), 429–447.Suche in Google Scholar
[4] Butkovičová, E.: Ultrafilters without immediate predecessors in Rudin-Frolík 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 βℕ without an infimum in Rudin-Frolík order, Proc. of the 11th Winter School on Abstract Analysis (Železná Ruda, 1983), Rend. Circ. Mat. Palermo (2) (1984), Suppl. no. 3, 75–80.Suche in Google Scholar
[7] Butkovičová, E.: Decreasing chains without lower bounds in the Rudin-Frolík order, Proc. 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, Springer 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. 102821.10.1016/j.apal.2020.102821Suche in Google Scholar
[11] Hart, K. P.: Long chains in the Rudin-Frolík order for uncountable cardinals, https://arxiv.org/pdf/2303.14252 (2024).Suche in Google Scholar
[12] Jech, T.: Set Theory. 3rd millennium edition, revised and expanded. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Suche in Google Scholar
[13] Jureczko, J.: Ultrafilters without immediate predecessors in Rudin-Frolík order for regulars, Results Math. 77 (2022), Art. 230.10.1007/s00025-022-01762-wSuche in Google Scholar
[14] Jureczko, J.: Chains in the Rudin-Frolík order for regulars, Raporty Katedry Telekomunikacji i Teleinformatyki, 2022; dona.pwr.edu.plSuche in Google Scholar
[15] Jureczko, J.: A note on special subsets of the Rudin-Frolík orderfor regulars, Math. Slovaca 73(4) (2023), 825–834.10.1515/ms-2023-0060Suche in Google Scholar
[16] Jureczko, J.: Decreasing chains without lower bounds in the Rudin Frolík order for regulars, https://arxiv.org/pdf/2304.01398.pdfSuche in Google Scholar
[17] Jureczko, J.: On some constructions of ultrafilters over a measurable cardinal, in preparation.Suche in Google Scholar
[18] Kanamori, A.: Ultrafilters over a measurable cardinal, Ann. Math. Logic 11 (1976), 315–356.10.1016/0003-4843(76)90012-7Suche in Google Scholar
[19] Kunen, K.: Set Theory, London, UK: College Publications, 2011.Suche in Google Scholar
[20] Kunen, K.: Weak P-points in ℕ* Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978), pp. 741–749, Colloq. Math. Soc. Jnos Bolyai, 23, North-Holland, Amsterdam-New York, 1980.Suche in Google Scholar
[21] Rudin, M. E.: Types of Ultrafilters. In: Topology Seminar Wisconsin 1965, Princeton Universiy Press, 1966.10.1515/9781400882076-021Suche in Google Scholar
[22] Rudin, M. E.: Partial orders on the types in βℕ, Trans. Amer. Math. Soc. 155 (1971), 353–362.10.2307/1995690Suche in Google Scholar
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Artikel in diesem Heft
- Algebraic structures formalizing the logic of effect algebras incorporating time dimension
- Walks on tiled boards
- Composition on FLew-algebras
- On high power sums of a hybrid arithmetic function
- On indices of quintic number fields defined by x5 + ax + b
- Note on fundamental system of solutions to the differential equations (D2 − 2Dα + α2 ± β2) y = 0
- Several sharp inequalities involving (hyperbolic) tangent, tanc, cosine, and their reciprocals
- A new Approach of Generalized Fractional Integrals in Multiplicative Calculus and Related Hermite–Hadamard-Type Inequalities with Applications
- On a periodic problem for super-linear second-order ODEs
- Existence and Uniqueness of Solutions for Fractional Dynamic Equations with Impulse Effects
- Periodic Solutions for Conformable Non-autonomous Non-instantaneous Impulsive Differential Equations
- Self referred equations with an integral boundary condition
- Approximation by matrix means of double Vilenkin-Fourier series
- Maps on self-adjoint operators preserving some relations related to commutativity
- Chains in the Rudin-Frolík order
- Relative versions of first and second countability in hyperspaces
- Proportion estimation in multistage pair ranked set sampling
- The Marshall-Olkin Extended Gamma Lindley distribution: Properties, characterization and inference
