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Tensor products of $$D$$-posets and $$D$$-test spaces. (English) Zbl 0830.03031
A $$D$$-poset (or a difference poset) is a poset $$L$$ with the greatest element 1 and a partial binary operation $$\ominus: L\times L\to L$$ such that $$b\ominus a$$ is defined iff $$a\leq b$$ and, for $$a,b, c\in L$$, we have (i) $$b\ominus a\leq b$$; (ii) $$(b\ominus (b\ominus a))=a$$; (iii) if $$a\leq b\leq c$$, then $$c\ominus b\leq c\ominus a$$ and $$(c\ominus a) \ominus (c\ominus b)= b\ominus a$$. For any $$D$$-poset, there exists a $$D$$- test space [the authors, Rep. Math. Phys. 34, 151-170 (1994; Zbl 0820.03038)]. Using this representation, a tensor product and a state tensor product of $$D$$-posets is introduced and studied, and some examples are presented.

##### MSC:
 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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##### References:
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