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Definability in infinitary languages and invariance by automorphims

Rodrigues A. A. M., Miranda Filho R. C., de Souza E. G.

Reports on Mathematical Logic

2010

Vol. 45

119-133

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.