axiomatic set theory

Axiomatic set theory is a branch of mathematical logic that studies sets and their relationships by formulating precise axioms to avoid paradoxes and provide a rigorous foundation for mathematics.

Aliases (7)

• conservative extension of Zermelo–Fraenkel set theory ×1
• first-order theory ×1
• second-order set theory ×1
• set theory ×1
• set theory axiom ×1
• set-theoretic axiom ×1
• two-sorted first-order theory ×1

Instances (12)

• Zermelo–Fraenkel set theory
• von Neumann–Bernays–Gödel set theory
• ZF
• axiom schema of separation ("set theory axiom")
• Zermelo set theory
• axiom of choice ("set-theoretic axiom")
• Morse–Kelley set theory by class–set distinction