Abstract
In his thesis Para uma Teoria Geral dos Homomorfismos (1944), the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we tried to keep in mind, so much as possible, the gist of his standpoint.
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References
Bourbaki, N., Theory of Sets, London-Ontario: Hermann, Addison Wesley, 1968.
Bouscaren E. (eds) (1998) Model Theory and Algebraic Geometry: An Introduction to E. Hrushovski’s Proof of the Geometric Mordell-Lang Conjecture. Springer-Verlag, New York
da Costa N.C.A. and Chuaqui R. (1988) ‘On Suppes set-theoretical predicates’. Erkenntnis 29:95–112
Hodges W. (1997). A Shorter Model Theory. Cambridge, Cambridge University Press
Hrushovski E. (1996). ‘The Mordell-Lang conjecture for function fields’. Journal Am. Math. Soc. 9:667–690
Krasner M. (1938). ‘Une généralisation de la notion de corps’. Journal de Math. Pures et Appl. 17:367–385
Krasner, M., ‘Endothéorie de Galois abstraite’, Séminaire Dubreil-Pisot, Alg. et Théorie des Nombres 22, 6, 1968-69
Marker D. (2002). Model Theory: An Introduction. New York, Springer-Verlag
Marshall M.V., Chuaqui R. (1991) ‘Sentences of type theory: the only sentences preserved under isomorphisms’. Journal of Symb. Logic 56:932–948
Pillay A. (1983) An Introduction to Stability Theory. Oxford: Oxford Sci. Pu.
Pillay A. (1996) Geometric Stability Theory. Oxford: Oxford Sci. Pu.
Sebastião e Silva, J., ‘Para Uma Teoria Geral Dos Homomorfismos (Thesis)’, in J. C. Ferreira, J. S. Guerreiro and J. S. Oliveira (eds.), Obras de José Sebastião e Silva, Volume 1, Lisbon: Instituto Nacional de Investigação Científica, 1985, pp. 135–339.
Sebastião e Silva J. (1945). ‘Sugli automorfismi di un sistema matematico qualunque’. Comm. Pontif. Acad. Sci. 9:327–357
Sebastião e Silva J. (1985). ‘On automorphisms of arbitrary mathematical systems’. History and Philosophy of Logic 6:91–116
Tarski A. (1983) Logic, Semantics, Metamathematics. Indianapolis: Hackett
Tarski A. (1986). ‘What are logical notions?’. History and Philosophy of Logic 7:143–154
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da Costa, N.C.A., Rodrigues, A.A.M. Definability and Invariance. Stud Logica 86, 1–30 (2007). https://doi.org/10.1007/s11225-007-9049-6
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DOI: https://doi.org/10.1007/s11225-007-9049-6