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The equivalence of a generalized Martin's axiom to a combinatorial principle

Published online by Cambridge University Press:  12 March 2014

William Weiss
William Weiss*
Affiliation:
University of Toronto, Erindale College, Mississauga L5L IC6, Canada
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Abstract

A generalized version of Martin's axiom, called BACH, is shown to be equivalent to one of its combinatorial consequences, a generalization of P(c).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 4 , December 1981 , pp. 817 - 821
Copyright
Copyright © Association for Symbolic Logic 1981

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References

REFERENCES

[1]Baumgartner, J., Generalizing Martin's Axiom, Proceedings of the Cambridge Summer School in Set Theory (Mathias, A., Editor).Google Scholar
[2]Bell, M. G., On the combinatorial principle P(c)Fundamenta Mathematicae (to appear).Google Scholar
[3]Burke, D. K. and van Douwen, E. K., On countably compact extensions of normal locally compact M-spaces, Set-theoretic topology (Reed, G. M., Editor), Academic Press, New York, 1977.Google Scholar
[4]Comfort, W. W. and Negrepontis, S., The theory of ultrafilters, Springer-Verlag, Heidelberg, 1974.CrossRefGoogle Scholar
[5]Jech, T. J., Set theory, Academic Press, New York, 1977.Google Scholar
[6]Kunen, K. and Tall, F. D., Between Martin's axiom and Suslin's hypothesis, Fundamenta Mathematicae 102 (1979), 173–181.CrossRefGoogle Scholar
[7]MacNeille, H. M., Partially ordered sets, Transactions of the American Mathematical Society, vol. 42 (1937), pp. 416–460.CrossRefGoogle Scholar
[8]Martin, D. and Solovay, R. M., Internal Cohen extensions, Annals of Mathematical Logic, vol. 2 (1970), pp. 143–178.CrossRefGoogle Scholar
[9]Rothberger, F., On the property C and a problem of Hausdorff, Canadian Journal of Mathematics, vol. 4 (1952), pp. 111–116.CrossRefGoogle Scholar
[10]Rudin, M. E., Martin's axiom, Handbook of mathematical logic (Barwise, J., Editor), North-Holland, Amsterdam, 1978.Google Scholar
[11]Tall, F. D., Some applications of a generalized Martin's axiom, Transactions of the American Mathematical Society (to appear).Google Scholar