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1992 | 141 | 1 | 21-30
Tytuł artykułu

Representing free Boolean algebras

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Języki publikacji
EN
Abstrakty
EN
Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with $ℵ_1$ generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not a subalgebra of any partitioner algebra.
Słowa kluczowe
Rocznik
Tom
141
Numer
1
Strony
21-30
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-01-21
poprawiono
1991-08-19
Twórcy
autor
  • Department of Mathematics, York University, North York, Ontario, Canada M3J 1P3
autor
  • Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
Bibliografia
  • [1] B. Balcar, J. Pelant, and P. Simon, The space of ultrafilters on N covered by nowhere dense sets, Fund. Math. 110 (1980), 11-24.
  • [2] J. E. Baumgartner and M. Weese, Partition algebras for almost-disjoint families, Trans. Amer. Math. Soc. 274 (1982), 619-630.
  • [3] D. Booth, A Boolean view of sequential compactness, Fund. Math. 85 (1974), 99-102.
  • [4] A. Dow and R. Frankiewicz, Remarks on partitioner algebras, Proc. Amer. Math. Soc. 113 (1991), 1067-1070.
  • [5] A. Dow and P. Nyikos, Compact Hausdorff spaces with moderately large families of convergent sequences, preprint.
  • [6] S. Mr'owka, On completely regular spaces, Fund. Math. 41 (1954), 105-106.
  • [7] S. Mr'owka, Some set-theoretic constructions in topology, ibid. 94 (1977), 83-92.
  • [8] J. Roitman, Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom, ibid. 103 (1979), 47-60; Correction, ibid. 129 (1988), 141.
  • [9] F. Rothberger, On some problems of Hausdorff and of Sierpiński, ibid. 35 (1948), 29-46.
  • [10] J. Teresawa, Spaces N ∪ ℛ and their dimensions, Topology Appl. 11 (1980), 93-102.
  • [11] E. K. van Douwen, The integers and topology, in: Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, 1984, 111-168.
  • [12] J. Vaughan, Small uncountable cardinals and topology, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), North-Holland, 1990, 195-218.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv141i1p21bwm
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