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On boolean subalgebras of (ω1)/ctble

Published online by Cambridge University Press:  12 March 2014

Alan Dow
Alan Dow*
Affiliation:
Department of Mathematics, York University, North York, Ontario, M3J 1P3, Canada, E-mail: alan.dow@math.stat.yorku.ca
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Extract

It is well known that every Boolean algebra of size ω1 can be embedded into (ω)/fin. E. van Douwen proved that if CH failed then there is a Boolean algebra of size ω2 which cannot be embedded into (ω1)/ctble. We show that ◇ is equivalent to the statement that a certain natural Boolean algebra of size embeds into (ω1)/ctble. I would like to thank B. Velickovic for many helpful conversations.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 3 , September 1996 , pp. 873 - 879
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Shelah, S., On cardinal invariants of the continuum, Axiomatic set theory, Contemporary Mathematics, American Mathematical Society, 1984.Google Scholar
[2]van Douwen, E. K., On question Q47, Topology and its Applications, vol. 39 (1991), pp. 33–42.CrossRefGoogle Scholar