Posets of copies of countable scattered linear orders

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Abstract

We show that the separative quotient of the poset P(L), of isomorphic suborders of a countable scattered linear order L is σ-closed and atomless. So, under the CH, all these posets are forcing-equivalent (to (P(ω)/Fin)+).

MSC

06A05
06A10
03C15
03E40

Keywords

Scattered linear order
Isomorphic substructure
Denumerable structure
σ-closed poset
Forcing

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