Definability in infinitary languages and invariance by automorphims
Anderson Adão Rodrigues, Ricardo C. Miranda Filho, Edelcio Gonçalves de Souza · Reports on Mathematical Logic · 2010
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.