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On the permanence properties of interval homogeneous orthomodular lattices. (English) Zbl 1077.06005
An orthomodular lattice $$L$$ is called interval homogeneous if (i) it is $$\sigma$$-complete, and (ii) whenever it is isomorphic to some of its intervals $$[a,b]$$, then it is isomorphic to each of its intervals $$[c,d]\supseteq [a,b]$$. The class of all such lattices is denoted by Inthom. The authors remark that their investigation of this class was inspired by some results of Cantor-Bernstein type. A $$\sigma$$-complete orthomodular lattice is denoted as $$\sigma$$-OML.
Sample results: Inthom is a proper class (in fact, a stronger result concerning a subclass of Inthom is proved). The authors find sufficient conditions under which a $$\sigma$$-OML belongs to Inthom. Each $$\sigma$$-OML is a $$\sigma$$-epimorphic image of an element of Inthom. Further, each $$\sigma$$-OML is a $$\sigma$$-epimorphic image of a $$\sigma$$-OML which does not belong to Inthom. Analogous results are obtained when instead of $$\sigma$$-homomorphic images we deal with sub-$$\sigma$$-algebras.

##### MSC:
 06C15 Complemented lattices, orthocomplemented lattices and posets
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