(1) Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran;(2) School of Mathematics, Amirkabir University of Technology, Hafez avenue, 15194 Tehran, Iran
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.