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On the concreteness of quantum logics

Pavel Pták; John David Maitland Wright — 1985

Aplikace matematiky

It is shown that for any quantum logic $L$ one can find a concrete logic $K$ and a surjective homomorphism $f$ from $K$ onto $L$ such that $f$ maps the centre of $K$ onto the centre of $L$ . Moreover, one can ensure that each finite set of compatible elements in $L$ is the image of a compatible subset of $K$ . This result is “best possible” - let a logic $L$ be the homomorphic image of a concrete logic under a homomorphism such that, if $F$ is a finite subset of the pre-image of a compatible subset of $L$ , then $F$ is compatible....

On Kalmbach measurability

A. B. d' Andrea; P. de Lucia; John David Maitland Wright — 1994

Applications of Mathematics

In this note we show that, for an arbitrary orthomodular lattice $L$ , when $μ$ is a faithful, finite-valued outer measure on $L$ , then the Kalmbach measurable elements of $L$ form a Boolean subalgebra of the centre of $L$ .

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