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  1. ; (, Mathematica Slovaca)
    Abstract An irreducible complete atomicomlof 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, algebraicomlwith the 2-covering property, and Keller’s construction provides an example of an infinite-height, irreducible, completeomlthat has the covering property and is completely hereditarily atomic. Completely hereditarily atomicomlsgeneralize algebraicomls suitably to quantum predicate logic. 
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