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Partition properties of ω1 compatible with CH

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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.
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  • Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3, stevo@math.toronto.edu
  • Matematicki Institut, Kneza Mihaila 35, 11000 Beograd, Yugoslavia
Bibliografia
  • [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.
  • [1] W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Springer, Berlin, 1974.
  • [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.
  • [3] K. J. Devlin and H. Johnsbraten, The Souslin Problem, Lecture Notes in Math. 405, Springer, 1974.
  • [4] A. Dow, PFA and ω*, Topology Appl. 28 (1988), 127-140.
  • [5] F. Galvin, On Gruenhage's generalization of first countable spaces II, Notices Amer. Math. Soc. 24 (1977), A-257.
  • [6] F. Galvin, letters of November 12, 1980 and May 18, 1981.
  • [7] F. Hausdorff, Die Graduierung nach dem Endverlauf, Abh. König. Sächs. Gesell. Wiss. Math.-Phys. Kl. 31 (1909), 296-334.
  • [8] F. Hausdorff, Summen von $ℵ_1$ Mengen, Fund. Math. 26 (1936), 241-255.
  • [9] K. Kunen, (κ,λ*) gaps under MA, note of August 1976.
  • [10] M. Magidor and J. Malitz, Compact extensions of L(Q), Ann. Math. Logic 11 (1977), 217-261.
  • [11] J. van Mill and G. M. Reed, Open Problems in Topology, North-Holland, Amsterdam, 1990.
  • [12] A. Ostaszewski, On countably compact perfectly normal spaces, J. London Math. Soc. (2) 14 (1976), 505-516.
  • [13] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982.
  • [14] S. Todorčević, Forcing positive partition relations, Trans. Amer. Math. Soc. 280 (1983), 703-720.
  • [15] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294.
  • [16] S. Todorčević, Partition Problems in Topology, Contemp. Math. 84, Amer. Math. Soc., Providence, 1989.
  • [17] S. Todorčević, Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993), 130-167.
  • [18] N. M. Warren, Properties of Stone-Čech compactifications of discrete spaces, Proc. Amer. Math. Soc. 33 (1972), 599-606.
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bwmeta1.element.bwnjournal-article-fmv152i2p165bwm
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