Determinateness and partitions
HTML articles powered by AMS MathViewer
- by Karel Prikry PDF
- Proc. Amer. Math. Soc. 54 (1976), 303-306 Request permission
Abstract:
It is proved that the axiom of determinateness of Mycielski and Steinhaus for games in which players alternate in writing reals implies that $\omega \to (\omega )_2^\omega$ (i.e. for every partition of infinite sets of natural numbers into two classes there is an infinite set such that all its infinite subsets belong to the same class).References
- Erik Ellentuck, A new proof that analytic sets are Ramsey, J. Symbolic Logic 39 (1974), 163–165. MR 349393, DOI 10.2307/2272356
- Fred Galvin and Karel Prikry, Borel sets and Ramsey’s theorem, J. Symbolic Logic 38 (1973), 193–198. MR 337630, DOI 10.2307/2272055 A. R. D. Mathias, On a generalization of Ramsey’s theorem, Thesis, Bonn, 1968.
- Jan Mycielski, On the axiom of determinateness. II, Fund. Math. 59 (1966), 203–212. MR 210603, DOI 10.4064/fm-59-2-203-212
- John C. Oxtoby, The Banach-Mazur game and Banach category theorem, Contributions to the theory of games, vol. 3, Annals of Mathematics Studies, no. 39, Princeton University Press, Princeton, N.J., 1957, pp. 159–163. MR 0093741
- Jack Silver, Every analytic set is Ramsey, J. Symbolic Logic 35 (1970), 60–64. MR 332480, DOI 10.2307/2271156
- Robert M. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1–56. MR 265151, DOI 10.2307/1970696
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 303-306
- MSC: Primary 04A20; Secondary 04A25
- DOI: https://doi.org/10.1090/S0002-9939-1976-0453540-X
- MathSciNet review: 0453540