= Stationary encoding in an aleph-one-like dense order
{title2=$L_S=\sum_{\alpha<\omega_1}B_\alpha$}
For a subset $S$ of the nonzero countable limit ordinals, let $B_\alpha=1+\mathbb Q$ when $\alpha\in S$ and $B_\alpha=\mathbb Q$ otherwise. The <order sum> is an <aleph-one-like linear order> whose nonempty proper initial segments are $\mathbb Q$ or $\mathbb Q+1$. At the limit cut before block $\delta$, the complementary final segment has a least point exactly when $\delta\in S$. <Club agreement of countable filtrations> makes this condition invariant modulo a nonstationary difference. <Disjoint stationary subsets of omega-one> consequently supply $2^{\aleph_1}$ nonisomorphic orders.
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