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Ultrafilters on ω

  • James E. Baumgartner (a1)

Abstract

We study the I-ultrafilters on ω, where I is a a collection of subsets of a set X, usually ℝ or ω1. The I-ultrafilters usually contain the P-points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.

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[1] Booth, David, Ultrafilters on a countable set, Annals of Mathematical Logic, vol. 2 (1970), pp. 124.
[2] Comfort, W. W. and Negrepontis, S., The theory of ultrafilters, Springer Verlag, 1974.
[3] Hart, K. P. and van Mill, J., Open problems on βω, Open problems in topology, North-Holland, Amsterdam, 1990, pp. 97125.
[4] Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.
[5] van Douwen, E. K., Remote points, Dissertationes Mathematicae (1981), pp. 145.

Ultrafilters on ω

  • James E. Baumgartner (a1)

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