Definability in Infinitary Languages and Invariance by Automorphisms

Alexandre A.M. Rodrigues,

Ricardo C. Miranda Filho,

Edelcio G. de Souza

Abstrakt

Given a LE -structure E, where LE is an infinitary language, we show that and can be chosen in such way that every orbit of the group G of automorphisms of E is LE -definable. It follows that two sequences of elements of the domain D of E satisfy the same set of L -formulas if and only if they are in the same orbit of G.

Słowa kluczowe: Definability, invariance, automorphism, infinitary languages
References
[1] N. C. A. Da Costa and A. A. M. Rodrigues, Definability and invariance, Studia Logica 86 (2007), pp. 1–30. 
[2] C. Karp, Languages with Expressions of Infinite Length, North-Holland, 1964. 
[3] M. Krasner, Une g´en´eralisation de la notion de corps, Journal de Math´ematiques Pures et Appliqu´ees, ser. 9, 17 (1938), pp. 367–385. 
[4] A. A. M. Rodrigues, R. C. de Miranda Filho and E. G. de Souza, Invariance and set-theoretical operations in first order structures, Reports on Mathematical Logic 40 (2006), pp. 209–215. 
[5] H. Rogers Jr., Some problems of definability in recursive function theory, Sets, Models and Recursion Theory, J. N. Crossley (ed.), North-Holland, 1966, pp. 183–201. 
[6] J. Sebasti˜ao e Silva, On automorphisms of arbitrary mathematical systems, History and Philosophy of Logic 6 (1985), pp. 91–116.

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