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

Butterfield, Jeremy and Isham, Chris (2002) A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations. UNSPECIFIED.

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    Abstract

    We 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 D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (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).


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    Item Type: Other
    Additional Information: Published in: International Journal of Theoretical Physics, volume 41, 2002, pages 613-639.
    Keywords: Kochen-Specker theorem; von Neumann algebras; topos theory; interval-valuations; support of a state.
    Subjects: Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Jeremy Butterfield
    Date Deposited: 29 Aug 2004
    Last Modified: 07 Oct 2010 11:12
    Item ID: 1919
    Public Domain: No
    URI: http://philsci-archive.pitt.edu/id/eprint/1919

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