Definability in infinitary languages and invariance by automorphims

• Autorzy: Rodrigues A. A. M. , Miranda Filho R. C. , de Souza E. G.
• Języki publikacji: PL

Abstrakty

EN

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

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2010
• Tom: Vol. 45
• Strony: 119--133
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Rodrigues A. A. M.

autor

Miranda Filho R. C.

autor

de Souza E. G.

Bibliografia

• [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 generalisation de la notion de corps, Journal de Math´ematiques Pures et Appliquees, 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. Sebastião e Silva, On automorphisms of arbitrary mathematical systems, History and Philosophy of Logic 6 (1985), pp. 91–116.