In the following we first introduce all the axioms, with names, and then we define the two systems CZF and IZF. We also recall some choice principles which are compatible with constructive and …

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Feb 20, 2009 · Myhill and Friedman’s systems were subsequently modified by Aczel, to obtain a system, CZF (Constructive Zermelo-Fraenkel), that is fully compatible with the ZF language (Aczel 1978, …

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We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of …

CZF can be interpreted in Martin-L ̈of theory (ML1V), using a “sets as trees” interpretation (Aczel). In fact, CZF and ML1V have the same proof-theoretic strength.

CZF, Constructive Zermelo-Fraenkel Set Theory, is an axiomatization of set theory in intuitionistic logic strong enough to do much standard math-ematics yet modest enough in proof-theoretical strength to …

ZF as a predicative theory. As it turns out, CZF is proof-theoretically equivalent with Martin-L ̈of type theory ML1V, as well as KP (Kripke-Platek admissible set theory), ID (inductive definability), and a …

CZF is the CZodiac community's farming and rewards token. In addition to optional burns done by investors of Chrono Pools, the CZodiac treasury is currently buying and burning $400 of CZF every …

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