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The Arkhangel’skiĭ–Tall problem: a consistent counterexample

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We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel'skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in $[ω]^ω$, and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.
Słowa kluczowe
  • Department of Mathematics, Auburn University, Auburn, Alabama 36849, U.S.A.
  • Department of Mathematics, Auburn University, Auburn, Alabama 36849, U.S.A.
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  • [W3] S. Watson, Problems I wish I could solve, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), North-Holland, Amsterdam, 1990, 37-76.
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