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Semiproper forcing axiom implies Martin maximum but not PFA+

Published online by Cambridge University Press:  12 March 2014


Saharon Shelah
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

Abstract

We prove that MM (Martin maximum) is equivalent (in ZFC) to the older axiom SPFA (semiproper forcing axiom). We also prove that SPFA does not imply SPFA+ or even PFA+ (using the consistency of a large cardinal).


Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1987

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References

[1]Baumgartner, J., Applications of the proper forcing axiom, Handbook of set-theoretic topology (Kunen, K. and Vaughan, J. E., editors), North-Holland, Amsterdam, 1984, pp. 913959.CrossRefGoogle Scholar
[2]Foreman, M., Magidor, M. and Shelah, S., Martin maximum, saturated ideals and nonregular ultrafilters. I, Annals of Mathematics (to appear).Google Scholar
[3]Laver, R., Making the supercompactness of κ: indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol. 29 (1978), pp. 385388.CrossRefGoogle Scholar
[4]Shelah, S., Iterated forcing and changing cofinalities, Israel Journal of Mathematics, vol. 40 (1981), pp. 132.CrossRefGoogle Scholar
[5]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[6]Todorčević, S., Forcing positive partition relations, Transactions of the American Mathematical Society, vol. 280 (1983), pp. 703720.CrossRefGoogle Scholar

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Semiproper forcing axiom implies Martin maximum but not PFA+
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