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generalized toposes with many-valued logic subobject classifiers (Topic)

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 $ LM_n$, non-commutative lattices with $ n$ logical values, where $ n$ can also be chosen to be any cardinal, including infinity, etc.

Bibliography

1
Georgescu, G. and C. Vraciu. 1970, On the characterization of centered Łukasiewicz algebras., J. Algebra, 16: 486-495.
2
Georgescu, G. 2006, N-valued Logics and Łukasiewicz-Moisil Algebras, Axiomathes, 16 (1-2): 123-136.
3
Baianu, I.C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory. Bulletin of Mathematical Biology, 39: 249-258.
4
Baianu, I.C.: 2004a. Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint. Cogprints-Sussex Univ.
5
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).
6
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 .
7
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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See Also: algebraic category of $LM_n$-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 MSC03B50 (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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