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1997 | 152 | 1 | 21-41
Tytuł artykułu

Extending real-valued functions in βκ

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EN
Abstrakty
EN
An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality $\got c$ and that it is consistent that ω*\{p} is C*-embedded for some but not all p ∈ ω*.
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autor
  • Department of Mathematics, York University, North York, Ontario, Canada M5S 1A1, adow@yorku.ca
Bibliografia
  • [AS81] U. Avraham and S. Shelah, Martin's axiom does not imply that every two $ℵ_1$-dense sets of reals are isomorphic, Israel J. Math. 38 (1981), 161-176.
  • [BS87] A. Blass and S. Shelah, There may be simple $P_ℵ_1$ and $P_ℵ_2$-points and the Rudin-Keisler order may be downward directed, Ann. Pure Appl. Logic 83 (1987), 213-243.
  • [vDKvM] E. K. van Douwen, K. Kunen and J. van Mill, There can be proper dense C*-embedded subspaces in βω-ω, Proc. Amer. Math. Soc. 105 (1989), 462-470.
  • [Dow88] A. Dow, An introduction to applications of elementary submodels to topology, Topology Proc. 13 (1988), 17-72.
  • [Dow92] A. Dow, Set theory in topology, in: Recent Progress in General Topology, M. Hušek and J. van Mill (eds.), Elsevier, 1992, 169-197.
  • [DJW89] A. Dow, I. Juhász and W. Weiss, Integer-valued functions and increasing unions of first countable spaces, Israel J. Math. 67 (1989), 181-192.
  • [DM90] A. Dow and J. Merrill, $ω_2* - U(ω_2)$ can be C*-embedded in $βω_2$, Topology Appl. 35 (1990), 163-175.
  • [HvM90] K. P. Hart and J. van Mill, Open problems on βω, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), North-Holland, 1990, 97-125.
  • [Laf93] C. Laflamme, Bounding and dominating number of families of functions on ω, Math. Logic Quart. 40 (1994), 207-223.
  • [Mil84] A. Miller, Rational perfect set forcing, in: Axiomatic Set Theory, Contemp. Math. 31, 1984, 143-159.
  • [She84] S. Shelah, On cardinal invariants of the continuum, Axiomatic Set Theory, Contemp. Math. 31, 1984, 183-207.
  • [Tod89a] S. Todorčević, Partition Problems in Topology, Contemp. Math. 84, Amer. Math. Soc., 1989.
  • [Tod89b] S. Todorčević, Tightness in products, Interim Rep. Prague Topolog. Sympos. 4 (1989), 7-8.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv152i1p21bwm
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