Archive for Mathematical Logic 52 (5-6):525-541 (2013)

We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show that there is an homeomorphism between the space of types of norm less than 1 in this model companion, and the space of quasistates of the C*-algebra ${\mathcal{A}}$
Keywords Hilbert space   C*-algebra representation  Model theory  Stability theory  Types
Categories (categorize this paper)
DOI 10.1007/s00153-013-0330-2
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 54,715
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Hilbert Spaces Expanded with a Unitary Operator.Camilo Argoty & Alexander Berenstein - 2009 - Mathematical Logic Quarterly 55 (1):37-50.

Add more references

Citations of this work BETA

Forking and Stability in the Representations of a C*-Algebra.Camilo Argoty - 2015 - Journal of Symbolic Logic 80 (3):785-796.

Add more citations

Similar books and articles

Transfer Principle in Quantum Set Theory.Masanao Ozawa - 2007 - Journal of Symbolic Logic 72 (2):625 - 648.
Elimination of Algorithmic Quantifiers for Ordered Differential Algebra.Yunfu Shen - 1999 - Archive for Mathematical Logic 38 (3):139-144.
Pure-Injectivity and Model Theory for G-Sets.Ravi Rajani & Mike Prest - 2009 - Journal of Symbolic Logic 74 (2):474-488.
Distance Geometry and Geometric Algebra.Andreas W. M. Dress & Timothy F. Havel - 1993 - Foundations of Physics 23 (10):1357-1374.
Dividing in the Algebra of Compact Operators.Alexander Berenstein - 2004 - Journal of Symbolic Logic 69 (3):817-829.
Division Algebras and Quantum Theory.John C. Baez - 2012 - Foundations of Physics 42 (7):819-855.


Added to PP index

Total views
68 ( #142,659 of 2,386,633 )

Recent downloads (6 months)
4 ( #202,860 of 2,386,633 )

How can I increase my downloads?


My notes