DEPENDENCE LOGIC IN PREGEOMETRIES ANDω-STABLE THEORIES
Gianluca Paolini, Jouko Väänánen · Journal of Symbolic Logic · 2016
Abstract We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences concerning basic atomic independence statements are complete with respect to a variety of semantics. Our results show that the uses of independence concepts in as different areas as database theory, algebra, and model theory, can be completely characterized by the same axioms. We also consider concepts related to independence, such as dependence.