Abstract

Abstract An irreducible complete atomic oml of infinite height cannot be algebraic and have the covering property. However, modest departure from these conditions allows infinite-height examples. We use an extension of Kalmbach’s construction to the setting of infinite chains to provide an example of an infinite-height, irreducible, algebraic oml with the 2-covering property, and Keller’s construction provides an example of an infinite-height, irreducible, complete oml that has the covering property and is completely hereditarily atomic. Completely hereditarily atomic omls generalize algebraic omls suitably to quantum predicate logic.

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