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Title

The regular open algebra of βRR is not equal to the completion of P(ω)/fin

Authors 1

Affiliations

  1. Department of Mathematics, York University, North York, Ontario, Canada M3J 1P3

Abstract

Two compact spaces are co-absolute} if their respective regular open algebras are isomorphic (i.e. homeomorphic Gleason covers). We prove that it is consistent that βω\ω and βℝ\ℝ are not co-absolute.

Bibliography

  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. Baumgartner, Iterated forcing, in: Surveys in Set Theory, A. R. D. Mathias (ed.), Cambridge Univ. Press, 1983, 1-59.
  3. P. L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1987), 651-664.
  4. A. Dow, Tree π-bases for βN-N in various models, Topology Appl. 33 (1989), 3-19.
  5. A. Dow, Set theory in topology, in: Recent Progress in General Topology, M. Hušek and J. van Mill (eds.), Elsevier, 1992, 169-197.
  6. A. Dow and J. Zhou, On subspaces of pseudoradial spaces, Proc. Amer. Math. Soc., to appear.
  7. M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals (Ramat Gan, 1991), Israel Math. Conf. Proc., 6, Bar-Ilan Univ., Ramat Gan, 1993, 305-360.
  8. S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982.
  9. S. Shelah, On cardinal invariants of the continuum, in: Axiomatic Set Theory, Contemp. Math. 31, Amer. Math. Soc., 1984, 183-207.
  10. O. Spinas and S. Shelah, The distributivity numbers of P(ω)/fin and its squares, Number 494 of Shelah Archives.
  11. S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294.
  12. E. K. van Douwen, Transfer of information about βN-N via open remainder maps, Illinois J. Math. 34 (1990), 769-792.
  13. J. van Mill and S. W. Williams, A compact F-space not co-absolute with βℕ -ℕ, Topology Appl. 15 (1983), 59-64.
Fundamenta Mathematicae
1998/157/1
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Pages:
33-41
Main language of publication
English
Received
1997-05-10
Accepted
1997-10-15
Published
1998
Exact and natural sciences