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Existentially closed II1 factors

机译:存在封闭的II1因素

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摘要

We examine the properties of existentially closed (R-omega-embeddable) factors. In particular, we use the fact that every automorphism of an existentially closed (R-omega-embeddable) II1 factor is approximately inner to prove that Th(R) is not model complete. We also show that Th('R) is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th(R).
机译:我们研究了存在性封闭(R-Ω可嵌入)因子的特性。特别是,我们使用一个事实封闭的(可嵌入R-ω的)II1因子的每个自同构近似为内部的事实来证明Th(R)并非模型完全。我们还证明了Th('R)对于有限和无限强迫都是完整的,并使用后一结果证明存在连续的Th(R)的许多非同构存在闭合模型。

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