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Definability in Infinitary Languages and Invariance by Automorphisms

Publication date: 20.09.2010

Reports on Mathematical Logic, 2010, Number 45, pp. 119 - 133

Authors

,
Alexandre A.M. Rodrigues
University of Sao Paulo
, Brazil
All publications →
,
Ricardo C. Miranda Filho
Universidade Federal da Bahia, Bahia, Brasil
All publications →
Edelcio G. de Souza
Pontifical Catholic University of São Paulo, São Paulo, Brazil
All publications →

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Titles

Definability in Infinitary Languages and Invariance by Automorphisms

Abstract

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.

Keywords

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.

Information

Information: Reports on Mathematical Logic, 2010, Number 45, pp. 119 - 133

Article type: Original article

Titles:

Polish:

Definability in Infinitary Languages and Invariance by Automorphisms

English:

Definability in Infinitary Languages and Invariance by Automorphisms

Authors

University of Sao Paulo
Brazil

Universidade Federal da Bahia, Bahia, Brasil

Pontifical Catholic University of São Paulo, São Paulo, Brazil

Published at: 20.09.2010

Article status: Open

Licence: None

Percentage share of authors:

Alexandre A.M. Rodrigues (Author) - 33%
Ricardo C. Miranda Filho (Author) - 33%
Edelcio G. de Souza (Author) - 34%

Article corrections:

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Publication languages:

English

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