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 |
Keywords:
scattered linear order; isomorphic substructure; denumerable structure; \(\sigma\)-closed poset; forcingReferences:
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