= Suslin-tree obstruction to Martin's axiom
{c}
A <well-pruned set-theoretic tree> that is an <Aronszajn tree> and a <Suslin tree> gives a <forcing> with the <countable chain condition for forcing>: stronger nodes extend weaker ones. The $\omega_1$ <dense subsets of a forcing order> of nodes at or above each level cannot all be met by a <filter in an ordered set>, since that would produce a <cofinal branch>. Thus $\mathrm{MA}_{\aleph_1}$ fails. When the continuum exceeds $\aleph_1$, full <Martin axiom> includes this instance.
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