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
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.
Dow A., On the consistency of the Moore-Mrowka solution, Topology Appl., 44 (1992) 125–142.
Erdös P., Rado R., A partition calculus in set theory, Bull. Amer. Math. Soc., 62 (1956) 427–489.
Fremlin D.H., Consequences of Martin’s Maximum, Note of July 31, 1986.
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.
Jech T., Set Theory, Academic Press, New York, 1978.
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.
Nyikos P., Piatkiewicz L., On the equivalence of certain consequences of the proper forcing axiom, J. Symbolic Logic, 60 (1995) 431–443.
Shelah S., Proper forcing, Springer-Verlag, Berlin, 1982.
Todorcevic S., Forcing positive partition relations, Trans. Amer. Math. Soc., 280 (1983) 703–720.
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.
Todorcevic S., Directed sets and cofinal types, Trans. Amer. Math. Soc. 290 (1985) 711–723.
Todorcevic S., Partition problems in topology, Contemp. Math. 84, American Mathematical Society, 1989.
Todorcevic S., Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705 (1993) 130–167.
Todorcevic S., Random set mappings and separability of compacta, Topology Appl 74 (1996) 265–274.
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.
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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
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