By Berne B.J., Harp G.D.
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Extra resources for On the calculation of time correlation functions
3 in ). This is how (the algebraic representation of) intuitionistic logic manifests itself in a topos. Another, closely related fact is that the subobjects of any object A in a topos form a Heyting algebra. 2. Topos theory and physics A large part of the work on topos theory in physics consists in showing how states, physical quantities and propositions about physical quantities can be represented within a suitable topos attached to the system [5, 6, 7, 8]. The choice of topos will depend on the theory type (classical, quantum or, in future developments, even something completely new).
Phys. 106, (1986) 321  B. Schroer, Particle physics in the 60s and 70s and the legacy of contributions by J. A. 0371  B. Schroer, Ann. Phys. 295, (1999) 190  G. -J. Borchers, D. Buchholz and B. Schroer, Commun. Math. Phys. 219, (2001) 125, hep-th/0003243  S. ˚ Aks; Journ. Math. Phys. 6 (1965) 516  D. Buchholz and S. J. Summers, String– and Brane–Localized Causal Fields in a Strongly Nonlocal Model, arXiv:math-ph/0512060  H. Grosse and G. Lechner, JETP 11, (2007) 021  Works by Buchholz and Summers as well as by Grosse and Lechner, in preparation.
This point of view is expounded in detail in Bell’s book , which is our standard reference on these matters. Other excellent sources are  and part D of . The basic concept consists in deﬁning a formal language and then ﬁnding a representation of it in a suitable topos. As usual in mathematical logic, the formal language encodes the syntactic aspects of the theory and the representation provides the semantics. Topoi are a natural ‘home’ for the representation of formal languages encoding intuitionistic logic, more precisely, intuitionistic, higher-order, typed predicate logic with equality.
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