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generalized toposes with many-valued logic subobject classifiers
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Generalized topoi (toposes) with many-valued algebraic logic subobject classifiers are specified generically by the associated categories of algebraic logics, which were previously defined as  , non-commutative lattices with  logical values, where  can also be chosen to be any cardinal, including infinity, etc.
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- Georgescu, G. and C. Vraciu. 1970, On the characterization of centered Łukasiewicz algebras., J. Algebra, 16: 486-495.
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- Georgescu, G. 2006, N-valued Logics and Łukasiewicz-Moisil Algebras, Axiomathes, 16 (1-2): 123-136.
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- Baianu, I.C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory. Bulletin of Mathematical Biology, 39: 249-258.
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- Baianu, I.C.: 2004a. Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint. Cogprints-Sussex Univ.
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- Baianu, I.C.: 2004b Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics). CERN Preprint EXT-2004-059. Health Physics and Radiation Effects (June 29, 2004).
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- Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued Łukasiewicz Algebras in Relation to Dynamic Bionetworks, (M,R)-Systems and Their Higher Dimensional Algebra, Abstract and Preprint of Report in PDF .
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- Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006b, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., Axiomathes, 16 Nos. 1-2: 65-122.
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"generalized toposes with many-valued logic subobject classifiers" is owned by bci1. [ full author list (2) ]
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See Also: algebraic category of  -logic algebras, non-Abelian structures, abelian category, supplemental axioms for an Abelian category, higher dimensional generalized Van Kampen theorems (HD-VKT), axiomatic theory of supercategories and metacategories, categorical quantum logics: quantum LM-algebraic logic, non-commuting graph, non-Abelian structures, quantum logics toposes
| Other names: |
LMn-algebraic n-valued logic |
| Also defines: |
many-valued logic subobject classifier |
| Keywords: |
generalized topoi with many-valued logic subobject classifiers, the category of n-valued, LMn-logic algebras and LMn-lattice morphisms, n-valued logic algebra, algebraic catgeory of n-valued logic lattices and lattice-morphisms |
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Cross-references: infinity, cardinal, non-commutative, categories, generically, subobject classifiers, logic, algebraic, topoi
This is version 23 of generalized toposes with many-valued logic subobject classifiers, born on 2008-07-16, modified 2008-09-07.
Object id is 10803, canonical name is GeneralizedToposesTopoiWithManyValuedLogicSubobjectClassifiers.
Accessed 423 times total.
Classification:
| AMS MSC: | 03B50 (Mathematical logic and foundations :: General logic :: Many-valued logic) | | | 03G20 (Mathematical logic and foundations :: Algebraic logic :: Lukasiewicz and Post algebras) | | | 03G30 (Mathematical logic and foundations :: Algebraic logic :: Categorical logic, topoi) | | | 03B15 (Mathematical logic and foundations :: General logic :: Higher-order logic and type theory) | | | 18B25 (Category theory; homological algebra :: Special categories :: Topoi) | | | 58A03 (Global analysis, analysis on manifolds :: General theory of differentiable manifolds :: Topos-theoretic approach to differentiable manifolds) |
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Pending Errata and Addenda
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