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Chapter V Constructible Sets as Values of a Functor

DOI: 10.1016/s0049-237x(09)70056-4
  • Mathematics


Publisher Summary This chapter aims to show that, under suitable assumptions concerning the function B, the set CBπ(A)(a) is a value of a strongly definable functor. If a transitive model of Zermelo-Fraenkel (ZF) or of a suitable finitely axiomatizable subsystem of ZF is given, then within this model the property of its elements consisting in their being equal to CBxi(a) can be defined. The expression “within the model” means that the property and the class mentioned are defined by the means of the satisfiability in the model of an explicitly given formula. The theorems proved in the chapter allow establishing certain properties of constructible sets that cannot be derived directly from the definitions. Results are obtained using theorems on transfinite induction.

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