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 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.
@article{bwmeta1.element.bwnjournal-article-fmv141i1p21bwm,
author = {Alan Dow and P. Nyikos},
title = {Representing free Boolean algebras},
journal = {Fundamenta Mathematicae},
volume = {141},
year = {1992},
pages = {21-30},
zbl = {0807.54004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv141i1p21bwm}
}
Dow, Alan; Nyikos, P. Representing free Boolean algebras. Fundamenta Mathematicae, Tome 141 (1992) pp. 21-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv141i1p21bwm/
[00000] [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. | Zbl 0568.54004
[00001] [2] J. E. Baumgartner and M. Weese, Partition algebras for almost-disjoint families, Trans. Amer. Math. Soc. 274 (1982), 619-630. | Zbl 0515.03032
[00002] [3] D. Booth, A Boolean view of sequential compactness, Fund. Math. 85 (1974), 99-102. | Zbl 0297.54020
[00003] [4] A. Dow and R. Frankiewicz, Remarks on partitioner algebras, Proc. Amer. Math. Soc. 113 (1991), 1067-1070. | Zbl 0789.03043
[00004] [5] A. Dow and P. Nyikos, Compact Hausdorff spaces with moderately large families of convergent sequences, preprint.
[00005] [6] S. Mr'owka, On completely regular spaces, Fund. Math. 41 (1954), 105-106.
[00006] [7] S. Mr'owka, Some set-theoretic constructions in topology, ibid. 94 (1977), 83-92.
[00007] [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. | Zbl 0442.03034
[00008] [9] F. Rothberger, On some problems of Hausdorff and of Sierpiński, ibid. 35 (1948), 29-46. | Zbl 0032.33702
[00009] [10] J. Teresawa, Spaces N ∪ ℛ and their dimensions, Topology Appl. 11 (1980), 93-102.
[00010] [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.
[00011] [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.