Dependence of variables construed as an atomic formula

Wedefine a logicD capable of expressing dependence of a variable on designated variables only. Thus D has similar goals to the Henkin quantifiers of [4] and the independence friendly logic of [6] that it much resembles. The logic D achieves these goals by realizing the desired dependence declarations of variables on the level of atomic formulas. By [3] and [17], ability to limit dependence relations between variables leads to existential second order expressive power. OurD avoids somedifficulties arising in the original independence friendly logic from coupling the dependence declarations with existential quantifiers. As is the case with independence friendly logic, truth ofD is definable insideD. We give such a definition forD in the spirit of [11,2] and [1]. © 2009 Elsevier B.V. All rights reserved.