= Solution
<Martin's axiom> at $\kappa$, denoted $\mathrm{MA}_\kappa$, says that whenever a <forcing> order satisfies the <countable chain condition for forcing> and $\{D_\xi:\xi<\kappa\}$ is a family of dense <subsets>, there is a <filter in an ordered set> meeting every $D_\xi$. Equivalently, allow any family of at most $\kappa$ dense <subsets>. The <filter in an ordered set> is directed towards stronger common extensions and closed towards weaker conditions. \b[Full <Martin's axiom> requires $\mathrm{MA}_\kappa$ for every $\kappa<2^{\aleph_0}$.] The bound below the continuum is part of the usual full axiom, explaining its role in part (iv)(b).
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