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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
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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

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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