A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations

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dc.creatorButterfield, J.
dc.creatorIsham, C. J.
dc.date2001-07-24
dc.date.accessioned2026-07-07T06:02:29Z
dc.date.available2026-07-07T06:02:29Z
dc.descriptionWe extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth value to a proposition that the value of a quantity lies in a certain set $Δ\subseteq \mathR$. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectra (we call these `interval' valuations). There are two main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4).
dc.descriptionLatex2e
dc.identifierhttps://arxiv.org/abs/quant-ph/0107123
dc.identifierhttp://arxiv.org/abs/quant-ph/0107123
dc.identifierInt.J.Theor.Phys. 41 (2002) 613-639
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/89618
dc.subjectQuantum Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleA Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations
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