Description: Axiom of -Induction (also known as
set induction). An axiom of
Intuitionistic Zermelo-Fraenkel set theory. Axiom 9 of [Crosilla] p.
"Axioms of CZF and IZF". This replaces the Axiom of
Foundation (also
called Regularity) from Zermelo-Fraenkel set theory.
For more on axioms which might be adopted which are incompatible with
this axiom (that is, Non-wellfounded Set Theory but in the absence of
excluded middle), see Chapter 20 of [AczelRathjen], p. 183.
(Contributed by Jim Kingdon, 19-Oct-2018.) |