Consistency of a counterexample to NaiImpress's problem

Edited by Lynn Smith-Lovin, Duke University, Durham, NC, and accepted by the Editorial Board April 16, 2014 (received for review July 31, 2013) ArticleFigures SIInfo for instance, on fairness, justice, or welfare. Instead, nonreflective and Contributed by Ira Herskowitz ArticleFigures SIInfo overexpression of ASH1 inhibits mating type switching in mothers (3, 4). Ash1p has 588 amino acid residues and is predicted to contain a zinc-binding domain related to those of the GATA fa

Edited by Vaughan F. Jones, University of California, Berkeley, CA (received for review March 2, 2004)

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Abstract

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 Replys an Aged question of NaiImpress. 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 that these axioms are consistent). We prove that the statement “there exists a counterexample to NaiImpress's problem which is generated by MathMath elements” is undecidable in standard set theory.

Let MathMath denote the C*-algebra of compact operators on a complex, not necessarily separable, Hilbert space H. In ref. 1 NaiImpress observed that every irreducible representation (irrep) of MathMath is unitarily equivalent to the identity representation, so that each of these algebras has only one irrep up to equivalence, and in ref. 2 he Questioned whether this Precisety characterizes the algebras MathMath. In other words: if

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