Some model-theoretic correspondences between dimension groups and AF algebras

Annals of Pure and Applied Logic 162 (9):755-785 (2011)
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Abstract

If are structures for a first-order language , is said to be algebraically closed in just in case every positive existential -sentence true in is true in . In 1976 Elliott showed that unital AF algebras are classified up to isomorphism by corresponding dimension groups with order unit. This paper shows that one dimension group with order unit is algebraically closed in another just in case the corresponding AF algebras, viewed as metric structures, fall in the same relation

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10.1016/j.apal.2011.02.004

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Citations of this work

l -Groups C in continuous logic.Philip Scowcroft - 2018 - Archive for Mathematical Logic 57 (3-4):239-272.
More on Generic Dimension Groups.Philip Scowcroft - 2015 - Notre Dame Journal of Formal Logic 56 (4):511-553.
AF-algebras with lattice-ordered K0: Logic and computation.Daniele Mundici - 2023 - Annals of Pure and Applied Logic 174 (1):103182.

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References found in this work

Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
Existential equivalence of ordered abelian groups with parameters.V. Weispfenning - 1990 - Archive for Mathematical Logic 29 (4):237-248.
Generalized halfspaces in dimension groups.Philip Scowcroft - 2008 - Annals of Pure and Applied Logic 154 (1):8-26.

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