Abstract: A general formal language in which the value of formulas can be recursively defined can be given by a sextuple-model for n(2≤n≤_n )-valued logic. It constitutes a universal logic system UL ₁, which characterizes this kind of logic. Connectives like abstract negation, abstract implication and abstract equivalence can be defined in the system. They are the generalization of negation, implication and equivalence in two valued logic. Applying these connectives, the general forms of Russellian sets-making predicate and Curryian sets-making predicate were developed. In addition, a new type of set-making predicate which only contains equivalence was developed. Applying these three kinds of sets-making predicates, abstraction principle led to paradoxes in general system of finite valued logic, countable infinite valued logic and uncountable infinite valued logic.