Set theory is a branch of mathematics concerned with the study of sets, which are collections of objects. It serves as the foundation of modern mathematics and has numerous synonyms that are used to describe it. One of the most widely used alternative names is the theory of sets. This term is often used interchangeably with set theory, and it focuses on the investigation of the properties of sets. Another synonym would be set theory mathematics, which refers to the mathematical concepts and theories derived from the study of sets. Other alternative synonyms for set theory include the mathematical theory of sets and the study of collections. Regardless of the synonym used, set theory is a fundamental concept in mathematical study.