Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0597.46059
Mundici, Daniele
Interpretation of AF $C\sp*$-algebras in Łukasiewicz sentential calculus. (English)
[J] J. Funct. Anal. 65, 15-63 (1986). ISSN 0022-1236

It is well known that AF $C\sp*$-algebras can be classified completely by the corresponding dimension groups, i.e. the $K$-groups with an order unit. Interpreting the $K$-group $K\sb 0(A)$ of an AF $C\sp*$-algebra $A$ as a set of sequences in Łukasiewicz logic, the author gives a criterion for the simplicity of $A$ in terms of recursion-theoretic properties of $K\sb 0(A)$: If $A$ is Gödel complete in the sense that the set of consequence of a theory ``written in this language" is recursively enumerable but not recursive, then $A$ cannot be simple. In the case of the CAR algebra the corresponding set of sentences is explicitly worked out.
[H.Schröder]

MSC 2000:: *46L05 General theory of C*-algebras
46M20 Methods of algebraic topology in functional analysis
03B50 Many-valued logic
03G20 Post and Lukasiewicz algebras (algebraic logic)
06D30 De Morgan algebras and generalizations

Keywords: AF $C\sp*$-algebras; dimension groups; K-groups with an order; Łukasiewicz logic; recursion-theoretic properties of $K\sb 0(A)$; Gödel complete; CAR algebra

Cited in: Zbl 1209.06008 Zbl 1194.06008 Zbl 1194.06007 Zbl 1190.06009 Zbl 1172.06007 Zbl 1168.06007 Zbl 1183.06006 Zbl 1168.06006 Zbl 1154.06008 Zbl 1152.06008 Zbl 1153.06005 Zbl 1131.06011 Zbl 1125.03016 Zbl 1099.06006 Zbl 1078.06010 Zbl 1050.06006 Zbl 1046.03037 Zbl 1045.06004 Zbl 1045.06005 Zbl 1028.06006 Zbl 1027.06014 Zbl 0998.06010 Zbl 0992.06011 Zbl 0988.06008 Zbl 0987.06011 Zbl 0987.06012 Zbl 1016.06007 Zbl 0949.06003 Zbl 0942.06006 Zbl 0991.06008 Zbl 0937.06010 Zbl 0964.06009 Zbl 0920.06005 Zbl 0920.06004 Zbl 0876.06003 Zbl 0864.06004 Zbl 0864.06005 Zbl 0812.06010 Zbl 0827.06012 Zbl 0756.06005 Zbl 0753.03010 Zbl 0739.03038 Zbl 0715.46026 Zbl 0694.03017 Zbl 0658.06010 Zbl 0639.03043

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]