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.
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Bagheri, SM., Pourmahdian, M. The logic of integration. Arch. Math. Logic 48, 465–492 (2009). https://doi.org/10.1007/s00153-009-0133-7
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DOI: https://doi.org/10.1007/s00153-009-0133-7