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The measure algebra does not always embed

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The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.
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  • Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3, dowa@yorku.ca
  • Faculty of Information Technology and Systems, TU Delft, Postbus 5031, 2600 GA Delft, The Netherlands , k.p.hart@twi.tudelft.nl
Bibliografia
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  • [9] W. Just, A weak version of AT from OCA, in: Set Theory of the Continuum, H. Judah, W. Just and H. Woodin (eds.), Math. Sci. Res. Inst. Publ. 26, Springer, Berlin, 1992, 281-291.
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  • [11] N. N. Luzin, On subset of the series of natural numbers, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 403-410 (in Russian).
  • [12] J. van Mill, Weak P-points in Čech-Stone compactifications, Trans. Amer. Math. Soc. 273 (1982), 657-678.
  • [13] J. van Mill, An introduction to βω, in: Kunen and Vaughan [10], 503-568.
  • [14] I. I. Parovičenko [I. I. Parovichenko], A universal bicompact of weight ℵ, Soviet Math. Dokl. 4 (1963), 592-595; Russian original: Dokl. Akad. Nauk SSSR 150 (1963), 36-39.
  • [15] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, Berlin, 1982.
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  • [17] S. Shelah, Proper and Improper Forcing, Perspect. Math. Logic, Springer, Berlin, 1998.
  • [18] S. Todorčević, Partition Problems in Topology, Contemp. Math. 34, Amer. Math. Soc., Providence, RI, 1989.
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