The existence of mechanisms to describe and evaluate assertions in programming languages helps to reduce the conceptual gap existing between the specification and implementation phases in the software development, improving both tasks. Java, originally used as an Internet-oriented implementation language, is becoming a general-purpose language, which unfortunately does not provide this kind of mechanism. We present a proposal to include assertions into Java, which also allows including the use of quantified variables in the assertions. The paper analyzes the properties that such integration must satisfy in order to guarantee a seamless interaction with the rest of the language constructions. The proposal shows how assertions can be used to synchronize Java threads introducing the notion of synchronization object and extending the semantics of preconditions. The goal is to increase the object oriented expressiveness of the language to describe concurrency.