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Forcing Axioms

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Set Theory
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Abstract

This paper surveys combinatorial forcing axioms together with combinatorial and topological consequences and information about their consistency.

Research supported by NSERC. The author thanks the Centre de Recerca Matematica for financial support during his stay in Barcelona and the Department of Mathematics at the University of Wisconsin-Madison for its hospitality while this paper was being written.

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References

  1. Burke M.R., Liftings for Lebesgue measure, in: Set theory of the reals (Proceedings of a winter institute on set theory of the reals held at Bar-Ilan University, RamatGan (Israel), January 1991), (H. Judah, ed.), Israel Math. Conf. Proc. 6 (1993) 119–150.

    Google Scholar 

  2. Dow A., On the consistency of the Moore-Mrowka solution, Topology Appl., 44 (1992) 125–142.

    Article  MathSciNet  MATH  Google Scholar 

  3. Erdös P., Rado R., A partition calculus in set theory, Bull. Amer. Math. Soc., 62 (1956) 427–489.

    Article  MathSciNet  MATH  Google Scholar 

  4. Fremlin D.H., Consequences of Martin’s Maximum, Note of July 31, 1986.

    Google Scholar 

  5. Goldstern M., Tools for your forcing construction, in: Set theory of the reals (Proceedings of a winter institute on set theory of the reals held at Bar-Ilan University, Ramat-Gan (Israel), January 1991), (H. Judah, ed.) Israel Math. Conf. Proc., 6 (1993) 305–360.

    Google Scholar 

  6. Jech T., Set Theory, Academic Press, New York, 1978.

    Google Scholar 

  7. Laver R., Partition relations for uncountable cardinals ≤ 2nR°, in: Infinite and finite sets, (A. Hajnal, R. Rado, and V. Sós, eds.), Colloq. Math. Soc. János Bolyai 10 vol. II, 1975.

    Google Scholar 

  8. Nyikos P., Piatkiewicz L., On the equivalence of certain consequences of the proper forcing axiom, J. Symbolic Logic, 60 (1995) 431–443.

    Article  MathSciNet  MATH  Google Scholar 

  9. Shelah S., Proper forcing, Springer-Verlag, Berlin, 1982.

    Book  MATH  Google Scholar 

  10. Todorcevic S., Forcing positive partition relations, Trans. Amer. Math. Soc., 280 (1983) 703–720.

    Article  MathSciNet  MATH  Google Scholar 

  11. Todorcevic S., A note on the proper forcing axiom, in: Axiomatic set theory, (J.E. Baumgartner, D.A. Martin, and S. Shelah, eds.) Contemp. Math. 31, American Mathematical Society, 1984, 209–218.

    Chapter  Google Scholar 

  12. Todorcevic S., Directed sets and cofinal types, Trans. Amer. Math. Soc. 290 (1985) 711–723.

    Article  MathSciNet  MATH  Google Scholar 

  13. Todorcevic S., Partition problems in topology, Contemp. Math. 84, American Mathematical Society, 1989.

    Book  MATH  Google Scholar 

  14. Todorcevic S., Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993) 130–167.

    Article  MathSciNet  Google Scholar 

  15. Todorcevic S., Random set mappings and separability of compacta, Topology Appl 74 (1996) 265–274.

    Article  MathSciNet  MATH  Google Scholar 

  16. Velickovic B., Applications of the open coloring axiom, in: Set theory of the continuum, (H. Judah, W. Just and W.H. Woodin, eds), Math. Sci. Res. Inst. Publ. 26, Springer-Verlag, New York, (1992) 137–154.

    Chapter  Google Scholar 

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© 1998 Springer Science+Business Media Dordrecht

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Burke, M.R. (1998). Forcing Axioms. In: Di Prisco, C.A., Larson, J.A., Bagaria, J., Mathias, A.R.D. (eds) Set Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8988-8_1

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  • DOI: https://doi.org/10.1007/978-94-015-8988-8_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4978-0

  • Online ISBN: 978-94-015-8988-8

  • eBook Packages: Springer Book Archive

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