Abstract. We analyse logic actions of Polish groups which arise in continuous logic. We extend the generalised model theory of H.Becker from [3] to the case of Polish G-spaces when G is an arbitrary Polish group.
We make a more systematic study of the van Douwen diagram for cardinal coefficients related to combinatorial properties of partitions of natural numbers.
Generalizing model companions from model theory we define companions of pieces of canonical partitions of Polish G-spaces. This unifies several constructions from logic. The central problem of the paper is the existence of companions which form a G-orbit which is a G δ -set. We describe companions of some typical G-spaces.
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