Hostname: page-component-f554764f5-nwwvg Total loading time: 0 Render date: 2025-04-08T22:26:29.187Z Has data issue: false hasContentIssue false
  • English
  • Français

Forcing with stable posets

Published online by Cambridge University Press:  12 March 2014

Uri Avraham  and
Saharon Shelah
Uri Avraham
Affiliation:
Hebrew University, Jerusalem, Israel
Saharon Shelah
Affiliation:
Hebrew University, Jerusalem, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

The class of stable posets is defined and investigated. We give a forcing construction of a universe of set theory which satisfies a weak form of Martin's Axiom and 2ℵ0 > ℵ1 and yet some propositions which follow from CH hold in this universe.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 1 , March 1982 , pp. 37 - 42
Copyright
Copyright © Association for Symbolic Logic 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[A, S]Avraham, U. and Shelah, S., Martin's Axiom does not imply that every two ℵ1-dense sets of reals are isomorphic, Israel Journal of Mathematics, vol. 38 (1981), pp. 161–176.CrossRefGoogle Scholar
[B]Baumgartner, J. E., All ℵ1-dense sets of reals can be isomorphic, Fundamenta Mathematicae, vol. 79 (1973), pp. 101–106.CrossRefGoogle Scholar
[B, M, R]Baumgartner, J., Malitz, J. and Reinhardt, W., Embedding trees in the rationals, Proceedings of the National Academy of Sciences USA, vol. 67 (1970), pp. 1749–1753.CrossRefGoogle ScholarPubMed
[D, M]Dushnik, B. and Miller, E. W., Concerning similarity transformations of linearly ordered sets, Bulletin of the American Mathematical Society, vol. 46 (1940), pp. 322–326.CrossRefGoogle Scholar
[D, S1]Devlin, K. J. and Shelah, S., A weak version of ◊ which follows from , Israel Journal of Mathematics, vol. 29 (1978). pp. 239–247.CrossRefGoogle Scholar
[D, S2]Devlin, K. J. and Shelah, S., A note on the normal Moore conjecture, Canadian Journal of Mathematics, vol. 21, no. 2 (1979), pp. 241–251.CrossRefGoogle Scholar
[K, T]Kunen, K. and Tall, F.D., Between Martin's axiom and Souslin's hypothesis, Fundamenta Mathematicae, vol. 102 (1979), pp. 173–181.CrossRefGoogle Scholar
[M, S]Martin, D. A. and Solovay, R. M., Internal Cohen extensions, Annals of Mathematical Logic, vol. 2 (1970), pp. 143–178.CrossRefGoogle Scholar
[R1]Rothberger, F., On some problems of Hausdorf and of Sierpiński, Fundamenta Mathematicae, vol. 35 (1948), pp. 29–46.CrossRefGoogle Scholar
[R2]Rothberger, F., Eine Aquivalenz zwischen der Kontinuumhypothese und der Existenz der Lusinschen und Sierpińskischen Mengen, Fundamenta Mathematicae, vol. 30 (1938), pp. 215–217.CrossRefGoogle Scholar
[Si]Sierpinski, W., Sur les types d'ordres des ensembles linéaires, Fundamenta Mathematicae, vol. 37 (1950), pp. 253–264.CrossRefGoogle Scholar
[So, Te]Solovay, R. M. and Tennenbaum, S., Iterated Cohen extensions and Souslin's Problem, Annals of Mathematics, vol. 94 (1971), pp. 201–245.CrossRefGoogle Scholar