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

Alan Dow

Fundamenta Mathematicae (1998)

  • Volume: 157, Issue: 1, page 33-41
  • ISSN: 0016-2736

Abstract

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

How to cite

top

Dow, Alan. "The regular open algebra of βRR is not equal to the completion of P(ω)/fin." Fundamenta Mathematicae 157.1 (1998): 33-41. <http://eudml.org/doc/212276>.

@article{Dow1998,
abstract = {Two compact spaces are co-absoluteif their respective regular open algebras are isomorphic (i.e. homeomorphic Gleason covers). We prove that it is consistent that βω and βℝ are not co-absolute. },
author = {Dow, Alan},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {33-41},
title = {The regular open algebra of βRR is not equal to the completion of P(ω)/fin},
url = {http://eudml.org/doc/212276},
volume = {157},
year = {1998},
}

TY - JOUR
AU - Dow, Alan
TI - The regular open algebra of βRR is not equal to the completion of P(ω)/fin
JO - Fundamenta Mathematicae
PY - 1998
VL - 157
IS - 1
SP - 33
EP - 41
AB - Two compact spaces are co-absoluteif their respective regular open algebras are isomorphic (i.e. homeomorphic Gleason covers). We prove that it is consistent that βω and βℝ are not co-absolute.
LA - eng
UR - http://eudml.org/doc/212276
ER -

References

top
  1. [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. Zbl0568.54004
  2. [2] J. Baumgartner, Iterated forcing, in: Surveys in Set Theory, A. R. D. Mathias (ed.), Cambridge Univ. Press, 1983, 1-59. 
  3. [3] P. L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1987), 651-664. Zbl0637.03049
  4. [4] A. Dow, Tree π-bases for βN-N in various models, Topology Appl. 33 (1989), 3-19. Zbl0697.54003
  5. [5] A. Dow, Set theory in topology, in: Recent Progress in General Topology, M. Hušek and J. van Mill (eds.), Elsevier, 1992, 169-197. Zbl0796.54001
  6. [6] A. Dow and J. Zhou, On subspaces of pseudoradial spaces, Proc. Amer. Math. Soc., to appear. Zbl0909.54002
  7. [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. Zbl0834.03016
  8. [8] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, 1982. 
  9. [9] S. Shelah, On cardinal invariants of the continuum, in: Axiomatic Set Theory, Contemp. Math. 31, Amer. Math. Soc., 1984, 183-207. 
  10. [10] O. Spinas and S. Shelah, The distributivity numbers of P(ω)/fin and its squares, Number 494 of Shelah Archives. 
  11. [11] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294. Zbl0658.03028
  12. [12] E. K. van Douwen, Transfer of information about βN-N via open remainder maps, Illinois J. Math. 34 (1990), 769-792. Zbl0709.54020
  13. [13] J. van Mill and S. W. Williams, A compact F-space not co-absolute with βℕ -ℕ, Topology Appl. 15 (1983), 59-64. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.