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Extending states on finite concrete logics

Anna De Simone·Mirko Navara·Pavel Pták
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Abstract

In this note we collect several observations on state extensions. They may be instrumental to anyone who pursues the theory of quantum logics. In particular, we find out when extensions (resp. signed extensions) exist in the "concrete" concrete logic of all even-element subsets of an even-element set. We also mildly add to the study of difference-closed logics by finding an extension theorem for subadditive states.

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Anna De Simone, Mirko Navara, Pavel Pták. 2004-01-22. Extending states on finite concrete logics. https://arxiv.org/abs/math-ph/0311012

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