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Posets of copies of countable scattered linear orders. (English) Zbl 1297.06001
Summary: We show that the separative quotient of the poset $$\langle\mathbb P(L),\subset\rangle$$ of isomorphic suborders of a countable scattered linear order $$L$$ is $$\sigma$$-closed and atomless. So, under the CH, all these posets are forcing-equivalent (to $$(P(\omega)/\mathrm{Fin})^+)$$.

##### MSC:
 06A05 Total orders 03C15 Model theory of denumerable and separable structures 03E40 Other aspects of forcing and Boolean-valued models 03E50 Continuum hypothesis and Martin’s axiom 06A07 Combinatorics of partially ordered sets
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