Archive for Mathematical Logic 48 (5):465-492 (2009)

Abstract
We develop a model theoretic framework for studying algebraic structures equipped with a measure. The real line is used as a value space and its usual arithmetical operations as connectives. Integration is used as a quantifier. We extend some basic results of pure model theory to this context and characterize measurable sets in terms of zero-sets of formulas
Keywords Graded measure structure  Ultraproduct  Elementary embedding  Continuous logic  Definable set
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DOI 10.1007/s00153-009-0133-7
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References found in this work BETA

Continuous Model Theory.Chen Chung Chang - 1966 - Princeton: Princeton University Press.
Probability Logic.Douglas N. Hoover - 1978 - Annals of Mathematical Logic 14 (3):287.

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Citations of this work BETA

Random Variables and Integral Logic.Karim Khanaki & Seyed-Mohammad Bagheri - 2011 - Mathematical Logic Quarterly 57 (5):494-503.
Quantified Universes and Ultraproducts.Alireza Mofidi & Seyed-Mohammad Bagheri - 2012 - Mathematical Logic Quarterly 58 (1-2):63-74.
Haar Measure and Integral Logic.Karim Khanaki & Massoud Amini - 2012 - Mathematical Logic Quarterly 58 (4):294-302.

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