$\omega$-morasses, and a weak form of Martin’s axiom provable in $\textrm {ZFC}$
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- by Dan Velleman PDF
- Trans. Amer. Math. Soc. 285 (1984), 617-627 Request permission
Abstract:
We prove, in $\text {ZFC}$, that simplified gap-$1$ morasses of height $\omega$ exist. By earlier work on the relationship between morasses and forcing it immediately follows that a certain Martin’s axiom-type forcing axiom is provable in $\text {ZFC}$. We show that this forcing axiom can be thought of as a weak form of ${\text {MA}}_{\omega _1}$ and give some applications.References
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F. Hausdorff, Summen von ${\aleph _1}$ mengen, Fund. Math. 26 (1936), 241-255.
- Wilfrid Hodges and Saharon Shelah, Infinite games and reduced products, Ann. Math. Logic 20 (1981), no. 1, 77–108. MR 611395, DOI 10.1016/0003-4843(81)90012-7
- Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
- Dan Velleman, Simplified morasses, J. Symbolic Logic 49 (1984), no. 1, 257–271. MR 736620, DOI 10.2307/2274108
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 285 (1984), 617-627
- MSC: Primary 04A20; Secondary 03E40, 03E50
- DOI: https://doi.org/10.1090/S0002-9947-1984-0752494-5
- MathSciNet review: 752494