Abstract:
This paper is a survey of the interaction between the three-valued propositional calculus of Lukasiewicz-Post and the axiomatic versions of quadratic form theory over (semi-real) rings known as abstract real spectra and real semigroups. © 2008 The authors and IOS Press. All rights reserved.
Registro:
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Parte de libro
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Título: | The three-valued logic of quadratic form theory over real rings |
Autor: | Dickmann, M.; Petrovich, A. |
Filiación: | Equipe de Logique Mathématique (UMR 7056), CNRS - Université Paris VII, Projet Topologie et Géométrie Algébriques, Institut de Mathématiques de Jussieu (UMR 7586), 2, Place Jussieu - Case 7012, 75251 Paris Cedex 05, France Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
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Palabras clave: | Abstract order space; Abstract real spectrum; Post algebra; Real semigroup; Special group |
Año: | 2008
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Página de inicio: | 49
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Página de fin: | 67
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Título revista: | Andrzej Mostowski and Foundational Studies
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Título revista abreviado: | Andrzej Mostowski and Found. Stud.
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815860_v_n_p49_Dickmann |
Referencias:
- Mostowski, A., L'æuvre scientifique de Jan Lukasiewicz (1957) Fundamenta Math., 44, pp. 1-11
- Dickmann, M., Petrovich, A., Abstract Real Spectra (2002) Real Semigroups and Three-valued Logic, in: Séminaire de Structures Algébriques Ordonnées, 73, p. 33. , 2001-2002, F. Delon, M. Dickmann and D. Gondard, eds, Paris 7-CNRS Logique, February,(Extended abstract)
- Dickmann, M., Petrovich, A., Real Semigroups and Abstract Real Spectra. I, Contemporary Math (2004) Amer. Math. Soc., 344, pp. 99-119
- Dickmann, M., Petrovich, A., Real Semigroups and Abstract Real Spectra , p. 140. , tentative title, in preparation, approx; Marshall, M., Spaces of Orderings and Abstract Real Spectra (1996) Lecture Notes Math., 1636. , Springer- Verlag, Berlin
- Bröcker, L., Abstract real spectra (1994) Séminaire de Structures Algébriques Ordonnées, 49, p. 4. , 1992-1993, F.Delon, M. Dickmann, D. Gondard, eds, Paris 7-CNRS Logique, Prépublications, Paris
- Andradas, C., Bröcker, L., Ruiz, J., Constructible Sets in Real Geometry (1996) A Series of Modern Surveys in Mathematics, 33. , Springer-Verlag, Berlin, Heidelberg, New York
- Dickmann, M., Miraglia, F., Special Groups. Boolean-Theoretic Methods in the Theory of Quadratic Forms (2000) Memoirs Amer. Math. Soc., 689
- Dickmann, M., Miraglia, F., (2005), 77, p. 25. , Rings with Many Units and Special Groups, Séminaire de Structures Algébriques Ordonnées, 2003-2004, F. Delon, M. Dickmann, D. Gondard, eds., Paris 7-CNRS Logique, Prépublications, Paris; Coste, M., Roy, M.-F., La topologie du spectre réel, in: Ordered Fields and Real Algebraic Geometry (1982) Amer. Math. Soc., 8, pp. 27-59. , D. Dubois, T. Recio, eds, Contemporary Math
- Bochnak, J., Coste, M., Roy, M.-F., Géométrie algébrique réelle (1987) Ergeb. Math., 12. , Springer-Verlag, Berlin, Heidelberg, New York ,[English translation: Real Algebraic Geometry, Ergeb. Math. 36, Springer-Verlag (1998).]
- Dickmann, M., Applications of model theory to real algebraic geometry; a survey (1985) Lecture Notes Math., 1130, pp. 76-150. , Springer-Verlag
- Becker, E., On the real spectrum of a ring and its applications to semi-algebraic geometry (1986) Bulletin Amer. Math. Soc., 15, pp. 19-60
- Knebusch, M., An invitation to real spectra, in: Quadratic and Hermitean forms, Conf. Hamilton/Ont. 1983, CMS Conf. Proc. (1984) Amer. Math. Soc., 4, pp. 51-105
- Marshall, M., Real reduced multirings and multifields (2006) J. Pure Appl. Algebra, 205, pp. 452-468
- Dickmann, M., Anneaux de Witt abstraits et groupes spéciaux (1993), 42. , Séminaire de Structures Algébriques Ordonnées, 1991-1992, F. Delon, M. Dickmann, D. Gondard, eds, Paris 7-CNRS Logique, Prépublications, Paris; Lira, A., Les groupes spéciaux , 7, p. 1995. , Ph.D. Thesis, Univ. of Paris; Dickmann, M., Marshall, M., Miraglia, F., Lattice-ordered reduced special groups (2005) Annals Pure Appl. Logic, 32, pp. 27-49
- Prestel, A., Lectures on Formally Real Fields (1975) Monografias de Matemáticas, 22. , 1093 IMPA, Rio de Janeiro, [Reprinted in Lecture Notes Math., Springer, 1984]
- Dickmann, M., Miraglia, F., On quadratic forms whose total signature is zero mod 2n (1998) Inventiones Math., 133, pp. 243-278
- Dickmann, M., Miraglia, F., Lam's Conjecture (2003) Algebra Colloquium, 10, pp. 149-176
- Boicescu, V., Filipoiu, A., Georgescu, G., Rudeanu, S., Lukasiewicz-Moisil Algebras (1991) Annals of Discrete Mathematics, 49. , North Holland, Amsterdam
- Balbes, R., Dwinger, P., Distributive Lattices (1974), Univ. of Missouri Press; Lam, T.Y., Introduction to Quadratic Forms over Fields (2004) Amer. Math. Soc., 67. , Graduate Series in Mathematics
- Scharlau, W., (1985) Quadratic and Hermitian Forms, , Springer-Verlag, Berlin
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- Pierce, R.S., Modules over Commutative Regular Rings (1967) Memoirs Amer. Math. Soc., 70
Citas:
---------- APA ----------
Dickmann, M. & Petrovich, A.
(2008)
. The three-valued logic of quadratic form theory over real rings. Andrzej Mostowski and Foundational Studies, 49-67.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815860_v_n_p49_Dickmann [ ]
---------- CHICAGO ----------
Dickmann, M., Petrovich, A.
"The three-valued logic of quadratic form theory over real rings"
. Andrzej Mostowski and Foundational Studies
(2008) : 49-67.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815860_v_n_p49_Dickmann [ ]
---------- MLA ----------
Dickmann, M., Petrovich, A.
"The three-valued logic of quadratic form theory over real rings"
. Andrzej Mostowski and Foundational Studies, 2008, pp. 49-67.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815860_v_n_p49_Dickmann [ ]
---------- VANCOUVER ----------
Dickmann, M., Petrovich, A. The three-valued logic of quadratic form theory over real rings. Andrzej Mostowski and Found. Stud. 2008:49-67.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815860_v_n_p49_Dickmann [ ]