The phrase "sets one cap" means to decide on a particular course of action or to have a specific aim in mind. There are several synonyms for this phrase, including "determines," "resolves," "commits," "dedicates," "focuses," and "targets." Each of these words expresses the act of making a firm decision and working towards a specific goal. Whether you are setting your cap on a career path, a personal relationship, or a particular achievement, it is important to have a clear focus and determination to see it through. Using any of these synonyms will help you communicate your intentions with clarity and purpose.