An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.
@article{bwmeta1.element.doi-10_2478_s11533-013-0320-y,
author = {Andrzej Starosolski},
title = {Ordinal ultrafilters versus P-hierarchy},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {84-96},
zbl = {1326.03055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0320-y}
}
Andrzej Starosolski. Ordinal ultrafilters versus P-hierarchy. Open Mathematics, Tome 12 (2014) pp. 84-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0320-y/
[1] Baumgartner J.E., Ultrafilters on ω, J. Symbolic Logic, 1995, 60(2), 624–639 http://dx.doi.org/10.2307/2275854 | Zbl 0834.04005
[2] Brendle J., Between P-points and nowhere dense ultrafilters, Israel J. Math., 1999, 113, 205–230 http://dx.doi.org/10.1007/BF02780177 | Zbl 0938.03069
[3] Comfort W.W., Negrepontis S., The Theory of Ultrafilters, Grundlehren Math. Wiss., 211, Springer, Heidelberg-New York, 1974 | Zbl 0298.02004
[4] Daguenet M., Emploi des filtres sur N dans l’étude descriptive des fonctions, Fund. Math., 1977, 95(1), 11–33 | Zbl 0362.04006
[5] Dolecki S., Multisequences, Quaest. Math., 2006, 29(2), 239–277 http://dx.doi.org/10.2989/16073600609486162
[6] Dolecki S., Mynard F., Cascades and multifilters, In: Hyperspace Topologies and Applications, La Bussière, October 5–10, 1997, Topology Appl., 2002, 104(1–3), 53–65 | Zbl 0953.54003
[7] Dolecki S., Starosolski A., Watson S., Extension of multisequences and countably uniradial classes of topologies, Comment. Math. Univ. Carolin., 2003, 44(1), 165–181 | Zbl 1099.54024
[8] Frolík Z., Sums of ultrafilters, Bull. Amer. Math. Soc., 1967, 73(1), 87–91 http://dx.doi.org/10.1090/S0002-9904-1967-11653-7 | Zbl 0166.18602
[9] Grimeisen G., Gefilterte Summation von Filtern und iterierte Grenzprozesse. I, Math. Annalen, 1960, 141(4), 318–342 http://dx.doi.org/10.1007/BF01360766 | Zbl 0096.26201
[10] Grimeisen G., Gefilterte Summation von Filtern und iterierte Grenzprozesse. II, Math. Annalen, 1961, 144(5), 386–417 http://dx.doi.org/10.1007/BF01396535 | Zbl 0101.14805
[11] Katětov M., On descriptive classes of functions, In: Theory of Sets and Topology, VEB Deutscher Verlag der Wissenschaften, Berlin, 1972, 265–278
[12] Katětov M., On descriptive classification of functions, In: General Topology and its Relations to Modern Analysis and Algebra III, Prague, August 30–September 3, 1971, Academia, Prague, 1972, 235–242
[13] Ketonen J., On the existence of P-points in the Stone-Čech compactification of integers, Fund. Math., 1976, 92(2), 91–94 | Zbl 0339.54035
[14] Laflamme C., A few special ordinal ultrafilters, J. Symbolic Logic, 1996, 61(3), 920–927 http://dx.doi.org/10.2307/2275792 | Zbl 0871.04004
[15] van Mill J., An introduction to βω, In: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 503–567
[16] Starosolski A., Fractalness of supercontours, In: Spring Topology and Dynamical Systems Conference, Topology Proc., 2006, 30(1), 389–402 | Zbl 1131.54020
[17] Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214 http://dx.doi.org/10.2178/jsl/1230396914
[18] Starosolski A., Cascades, order and ultrafilters, preprint avilable at http://arxiv.org/pdf/1201.2146.pdf