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This article gives a summary of the author's Ph.D. dissertation (arXiv:1609.06297). In addition to an overview of notions and results, it also provides sketches of various proofs and simplified presentations of certain abstract results of the dissertation, that concern tree representations of structures. Further, some extensions of the dissertation results are presented. These include the connections of the model-theoretic notions introduced in the thesis with fixed parameter tractability andarXiv:1811.01014v1 fatcat:vurmh3kcrbgtve7yp6lqngflpy