constructive set theory

Constructive set theory is a foundation for mathematics emphasizing the creation and explicit construction of sets rather than relying on non-constructive existence proofs. It focuses on mathematical objects that can be explicitly built or described, ensuring that existence claims are verified by providing a method to find or construct the object. This approach aligns with constructive logic, which avoids assumptions like the law of excluded middle, leading to a view of mathematics grounded in tangible, verifiable constructions rather than abstract existence assertions. It’s used to develop mathematics in a way that emphasizes explicit methods and constructive reasoning.