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We analyze the notion of weak elimination of hyperimaginaries (WEHI) insimple theories. A key observation in the analysis is a characterization ofWEHI in terms of forking dependence -- a condition we dubdependence-witnessed-by-imaginaries (DWIP). Generalizing results of [1] and[3], we show that in a simple theory with WEHI, forking and thorn-forkingcoincide. We also show that, conversely, the equivalence of independence andthorn-independence is (almost) sufficient for WEHI. Thus, the WEHI and thestatement independence = thorn-independence are morally equivalent. As afurther application of our technology, we demonstrate stable forking for1-based theories of finite SU-rank that have WEHI.

On Weak Elimination of Hyperimaginaries and its Consequences