A combinatorial statement concerning ideals of countable subsets of ω is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω, ω*)-gaps are Hausdorff, and that every coherent sequence on ω either almost includes or is orthogonal to some uncountable subset of ω.
@article{bwmeta1.element.bwnjournal-article-fmv152i2p165bwm,
author = {Uri Abraham and Stevo Todor\v cevi\'c},
title = {Partition properties of $\omega$1 compatible with CH},
journal = {Fundamenta Mathematicae},
volume = {154},
year = {1997},
pages = {165-181},
zbl = {0879.03015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv152i2p165bwm}
}
Abraham, Uri; Todorčević, Stevo. Partition properties of ω1 compatible with CH. Fundamenta Mathematicae, Tome 154 (1997) pp. 165-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv152i2p165bwm/
[00000] [0] U. Abraham, K. J. Devlin and S. Shelah, The consistency with CH of some consequences of Martin's axiom plus non-CH, Israel J. Math. 31 (1978), 19-33. | Zbl 0382.03040
[00001] [1] W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Springer, Berlin, 1974.
[00002] [2] H. G. Dales and W. H. Woodin, An Introduction to Independence for Analysts, London Math. Soc. Lecture Note Ser. 115, Cambridge University Press, 1987.
[00003] [3] K. J. Devlin and H. Johnsbraten, The Souslin Problem, Lecture Notes in Math. 405, Springer, 1974. | Zbl 0289.02043
[00004] [4] A. Dow, PFA and ω*, Topology Appl. 28 (1988), 127-140.
[00005] [5] F. Galvin, On Gruenhage's generalization of first countable spaces II, Notices Amer. Math. Soc. 24 (1977), A-257.
[00006] [6] F. Galvin, letters of November 12, 1980 and May 18, 1981.
[00007] [7] F. Hausdorff, Die Graduierung nach dem Endverlauf, Abh. König. Sächs. Gesell. Wiss. Math.-Phys. Kl. 31 (1909), 296-334. | Zbl 40.0446.02
[00008] [8] F. Hausdorff, Summen von Mengen, Fund. Math. 26 (1936), 241-255.
[00009] [9] K. Kunen, (κ,λ*) gaps under MA, note of August 1976.
[00010] [10] M. Magidor and J. Malitz, Compact extensions of L(Q), Ann. Math. Logic 11 (1977), 217-261.
[00011] [11] J. van Mill and G. M. Reed, Open Problems in Topology, North-Holland, Amsterdam, 1990. | Zbl 0718.54001
[00012] [12] A. Ostaszewski, On countably compact perfectly normal spaces, J. London Math. Soc. (2) 14 (1976), 505-516. | Zbl 0348.54014
[00013] [13] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982.
[00014] [14] S. Todorčević, Forcing positive partition relations, Trans. Amer. Math. Soc. 280 (1983), 703-720. | Zbl 0532.03023
[00015] [15] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294. | Zbl 0658.03028
[00016] [16] S. Todorčević, Partition Problems in Topology, Contemp. Math. 84, Amer. Math. Soc., Providence, 1989. | Zbl 0659.54001
[00017] [17] S. Todorčević, Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993), 130-167.
[00018] [18] N. M. Warren, Properties of Stone-Čech compactifications of discrete spaces, Proc. Amer. Math. Soc. 33 (1972), 599-606. | Zbl 0241.54016