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  1. Some model-theoretic correspondences between dimension groups and AF algebras.Philip Scowcroft - 2011 - Annals of Pure and Applied Logic 162 (9):755-785.
    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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  • Generalized Halfspaces in the Mixed-Integer Realm.Philip Scowcroft - 2009 - Notre Dame Journal of Formal Logic 50 (1):43-51.
    In the ordered Abelian group of reals with the integers as a distinguished subgroup, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The result is uniform in the integer coefficients and moduli of the initial generalized halfspaces.
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