Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-07T16:21:09.488Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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.)

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