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We study a natural subclass of continuous actions of Polish groups on Polish spaces which we call eventually open actions. We prove that this property characterizes the actions endowed with a complete system of hereditarily countable invariant structures introduced by Hjorth as a generalization of Scott sentences. [ABSTRACT FROM AUTHOR]

Let G be a closed subgroup of S∞ and X be a Polish G -space. To every x ∈ X we associate an admissible set Ax and show how questions about X which involve Baire category can be formalized in Ax. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

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 Gδ-set. We describe companions of some typical G-spaces. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]