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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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