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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

$ \omega $-morasses, and a weak form of Martin's axiom provable in $ {\rm ZFC}$


Author: Dan Velleman
Journal: Trans. Amer. Math. Soc. 285 (1984), 617-627
MSC: Primary 04A20; Secondary 03E40, 03E50
MathSciNet review: 752494
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Abstract: We prove, in 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 ZFC. We show that this forcing axiom can be thought of as a weak form of $ {\text{MA}}_{\omega_1}$ and give some applications.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0752494-5
PII: S 0002-9947(1984)0752494-5
Keywords: Morass, Martin's axiom
Article copyright: © Copyright 1984 American Mathematical Society