Algebraic closure in continuous logic

WARD HENSON, C.; TÉLLEZ, HERNANDO

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.41 suppl.1 Bogotá Oct. 2007

Algebraic closure in continuous logic

C. WARD HENSON¹, HERNANDO TÉLLEZ²
¹Department of Mathematics, University of Illinois, Urbana-Champaign, USA. E-mail: henson@math.uiuc.edu
²Department of Mathematics, University of Illinois, Urbana-Champaign, USA. E-mail: htellez@math.uiuc.edu

Abstract

We study the algebraic closure construction for metric structures in the setting of continuous first order logic. We give several characterizations of algebraicity, and we prove basic properties analogous to ones that algebraic closure satisfies in classical first order logic.

Key words: Continuous logic, metric structures, algebraic closure.

2000 Mathematics Subject Classification: Primary: 0C3xx. Secondary: 03C90, 03B50.

Resumen

Estudiamos la construcción de la clausura algebraica para estructuras métricas en el contexto de la lógica continua de primer orden. Damos varias caracterizaciones de algebricidad y probamos propiedades básicas análogas a aquellas que satisface la clausura algebraica en lógica clásica de primer orden.

Palabras clave: Lógica continua, estructuras métricas, clausura algebraica.

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References

1 I. Ben Yaacov, A. Berenstein, C. W. Henson, & A. Usvyatsov, Model theory for metric structures, 109 pages, to appear in a Newton Institute volume, Lecture Notes series of the London Mathematical Society, Cambridge University Press. [ Links ]

2 I. Ben Yaacov, Simplicity in compact abstract theories. Journal of Symbolic Logic, 3 (2003) 2,163-191. [ Links ]

3 I. Ben Yaacov & A. Usvyatsov, Continuous first order logic and local stability, submitted. [ Links ]