超代数的弱消去及其结果
On Weak Elimination of Hyperimaginaries and its Consequences
摘要：
我们分析了简单理论中的弱超线性消除（WEHI）概念。分析中的一个关键观察结果是WEHI在分叉依赖方面的特征-我们称之为依赖性见证（DWIP）。本文推广了文[1]和[3]的结果，证明了在一个简单的WEHI理论中，分叉和刺分叉是一致的。我们还表明，相反，等价的独立性和刺独立性是（几乎）足够的WEHI。因此，WEHI和独立性=刺独立性的陈述在道德上是等价的。作为我们的技术的进一步应用，我们证明了稳定的分叉1为基础的有限SU-秩的理论，有WEHI。
英文摘要：
We analyze the notion of weak elimination of hyperimaginaries (WEHI) in simple theories. A key observation in the analysis is a characterization of WEHI in terms of forking dependence -- a condition we dub dependence-witnessed-by-imaginaries (DWIP). Generalizing results of [1] and [3], we show that in a simple theory with WEHI, forking and thorn-forking coincide. We also show that, conversely, the equivalence of independence and thorn-independence is (almost) sufficient for WEHI. Thus, the WEHI and the statement independence = thorn-independence are morally equivalent. As a further application of our technology, we demonstrate stable forking for 1-based theories of finite SU-rank that have WEHI.
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