Boolean-valued models of set theory

Target entity: Boolean-valued models of set theory
Context triple: [forcing (set theory), relatedTo, Boolean-valued models of set theory]

• A. Fraenkel–Mostowski permutation models
  Fraenkel–Mostowski permutation models are set-theoretic constructions using permutations of atoms to demonstrate the independence of certain choice principles from Zermelo–Fraenkel set theory.
• B. Set Theory and Its Logic
  Set Theory and Its Logic is a foundational work by W.V.O. Quine that develops set theory within a rigorous logical framework, exploring its axioms, paradoxes, and philosophical implications.
• C. Kripke–Platek set theory
  Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
• D. Cardinal Invariants on Boolean Algebras
  "Cardinal Invariants on Boolean Algebras" is a research monograph by set theorist J. Donald Monk that systematically studies cardinal characteristics associated with Boolean algebras and their connections to set theory and logic.
• E. von Neumann paradox in set theory
  The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Boolean-valued models of set theory
Target entity description: Boolean-valued models of set theory are generalized models in which each statement is assigned a truth value from a complete Boolean algebra, providing a powerful framework for analyzing independence results and constructing alternative set-theoretic universes.

• A. Fraenkel–Mostowski permutation models
  Fraenkel–Mostowski permutation models are set-theoretic constructions using permutations of atoms to demonstrate the independence of certain choice principles from Zermelo–Fraenkel set theory.
• B. Set Theory and Its Logic
  Set Theory and Its Logic is a foundational work by W.V.O. Quine that develops set theory within a rigorous logical framework, exploring its axioms, paradoxes, and philosophical implications.
• C. Kripke–Platek set theory
  Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
• D. Cardinal Invariants on Boolean Algebras
  "Cardinal Invariants on Boolean Algebras" is a research monograph by set theorist J. Donald Monk that systematically studies cardinal characteristics associated with Boolean algebras and their connections to set theory and logic.
• E. von Neumann paradox in set theory
  The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
• F. None of above. chosen