The notion of forking extension is introduced by Shelah, see
Saharon Shelah, Classification theory and the number of non-isomorphic models, revised edition, North-Holland (1990)
Artem Chernikov, Itay Kaplan, Saharon Shelah, On non-forking spectra, arxiv/1205.3101
Will Boney, Rami Grossberg, Forking in short and tame AECs, arxiv/1306.6562
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