Provable Forms of Martin's Axiom

@article{Shannon1990ProvableFO,
  title={Provable Forms of Martin's Axiom},
  author={Gary P. Shannon},
  journal={Notre Dame Journal of Formal Logic},
  year={1990},
  volume={31},
  pages={382-388}
}
It is shown that if Martin's Axiom (MA) is restricted to well-orderable sets, and if the countable antichain condition is replaced by either a finite antichain condition or a finite «Q-strong antichain» condition, then the resulting statements are forms of MA provable in ZF. Variations of these weak forms of MA are shown to be equivalent to the Axiom of Choice and some of its weak forms 

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