论文标题
具有超浮雕理论的操作员代数
Operator algebras with hyperarithmetic theory
论文作者
论文摘要
我们表明，以下运算符代数具有超弧度理论：超限II $ _1 $ _1 $ \ rabscal r $，$ l（γ）$ for $γ$有限地生成的具有可解决的单词问题的群体，$ c^*（$ c^*（γ）$ for $γ$ for $γ$，$ c^*$ c^*$ c^*up fin $ c^*up fil fil fil $ c（2^ω）$，和$ c（\ mathbb p）$（其中$ \ mathbb p $是pseudoarc）。我们还表明，Cuntz代数$ \ MATHCAL O_2 $具有超浮雕理论，只要Kirchberg嵌入问题具有肯定的答案。最后，我们证明，如果存在没有超氧化理论的生存关闭（E.C.）II $ _1 $ factor（resp。C$^*$ - 代数），那么E.C.的许多理论都有许多理论。 II $ _1 $因素（分别为E.C. C $^*$ - 代数）。
We show that the following operator algebras have hyperarithmetic theory: the hyperfinite II$_1$ factor $\mathcal R$, $L(Γ)$ for $Γ$ a finitely generated group with solvable word problem, $C^*(Γ)$ for $Γ$ a finitely presented group, $C^*_λ(Γ)$ for $Γ$ a finitely generated group with solvable word problem, $C(2^ω)$, and $C(\mathbb P)$ (where $\mathbb P$ is the pseudoarc). We also show that the Cuntz algebra $\mathcal O_2$ has a hyperarithmetic theory provided that the Kirchberg embedding problem has an affirmative answer. Finally, we prove that if there is an existentially closed (e.c.) II$_1$ factor (resp. C$^*$-algebra) that does not have hyperarithmetic theory, then there are continuum many theories of e.c. II$_1$ factors (resp. e.c. C$^*$-algebras).
