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We prove, in      ZFC \text {ZFC}      , that simplified gap-     1 1       morasses of height      ω  \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 \text {ZFC}      . We show that this forcing axiom can be thought of as a weak form of      MA ω  1 {\text {MA}}_{\omega _1}       and give some applications.

𝜔-morasses, and a weak form of Martin’s axiom provable in 𝑍𝐹𝐶