Towards a Paraconsistent Quantum Set Theory
Citations
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Cites background from "Towards a Paraconsistent Quantum Se..."
...Specifically, Eva [10] suggests the following definition....
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...1 V (Subcl(Σ)) Eva [10] suggests the possibility of connecting TQT and QST via the set-theoretic structure V (Subcl(Σ)), where Subcl(Σ) is equipped with the negation ∗ rather than the Heyting negation....
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...Eva [10] notes that defining [S]∗ = [S∗] implies that E and L are isomorphic not just as complete lattices, but also as complete ortholattices....
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...Until now, the tantalising prospect of unifying these two (kinds of) Q-worlds, non-distributive set theoretic QST and distributive topos-theoretic TQT, within a single formal setting has gone almost completely unexplored (the prospect was first tentatively suggested by Eva [10])....
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...Eva [10] establishes the following basic properties of the ∗ negation....
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4 citations
References
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"Towards a Paraconsistent Quantum Se..." refers methods in this paper
...In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani (see, for example, [14], [13], [10]), and topos quantum theory, as developed by Isham, Butterfield and Döring, amongst others (see, for example, [8], [6], [3])....
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156 citations
"Towards a Paraconsistent Quantum Se..." refers background or methods in this paper
...In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani (see, for example, [14], [13], [10]), and topos quantum theory, as developed by Isham, Butterfield and Döring, amongst others (see, for example, [8], [6], [3])....
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...In [13], it was shown that if B is an algebra of mutually compatible projection operators on some Hilbert space H, then R(B) is isomorphic to the set of all self adjoint operators on H whose spectral projections all lie in B....
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152 citations