Naimark问题一个反例的相合性
Consistency of a counterexample to Naimark's problem
摘要：
本文构造了一个C* 代数，它只有一个直到酉等价的不可约表示，但不同构于任何希尔伯特空间上的紧算子代数.这回答了奈马克的一个老问题。我们的构造使用了一种称为钻石原理的组合语句，该原理与集合论的标准公理一致，但无法从这些公理中证明（假设这些公理是一致的）。证明了在标准集合论中，“存在由$\aleph_1$元素生成的Naimark问题的反例”是不可判定的.
英文摘要：
We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but is not isomorphic to the algebra of compact operators on any Hilbert space. This answers an old question of Naimark. Our construction uses a combinatorial statement called the diamond principle, which is known to be consistent with but not provable from the standard axioms of set theory (assuming those axioms are consistent). We prove that the statement ``there exists a counterexample to Naimark's problem which is generated by $\aleph_1$ elements'' is undecidable in standard set theory.
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