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Definability in Infinitary Languages and Invariance by Automorphisms

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Rodrigues A. A. M., Filho R. C. M., de Souza E. G.
Reports on Mathematical Logic
|
2010
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vol. 45
PL
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.
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