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Creators/Authors contains: "Harding, John"

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  1. ; ; (, Algebra universalis)
    We show that the variety of monadic ortholattices is closed under MacNeille and canonical completions. In each case, the completion of L is obtained by forming an associated dual space X that is a monadic orthoframe. This is a set with an orthogonality relation and an additional binary relation satisfying certain conditions. For the MacNeille completion, X is formed from the non-zero elements of L, and for the canonical completion, X is formed from the proper filters of L. The corresponding completion of L is then obtained as the ortholattice of bi-orthogonally closed subsets of X with an additional operation defined through the binary relation of X. With the introduction of a suitable topology on an orthoframe, as was done by Goldblatt and Bimb´o, we obtain a dual adjunction between the categories of monadic ortholattices and monadic orthospaces. A restriction of this dual adjunction provides a dual equivalence. 
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    Free, publicly-accessible full text available May 1, 2026
  2. ; (, 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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  3. ; ; ; ; ; ; ; ; ; ; et al (, Faraday Discussions)
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