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edited Dec 20, 2019 at 18:29

Is Can Ackerman set theory without class construction scheme plus a limitation of size axiom can prove consistency of ZF?

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asked Dec 20, 2019 at 18:23

Take all axioms of Ackermann's set theory, remove the class construction axiom schema.

Add the limitation of size axiom:

$\forall X \forall Y [X \in V \land Y \subseteq V \land |Y|\leq |X| \to Y \in V]$

Would the resulting theory prove $V$ to be a model of $\sf ZF$?

set-theory lo.logic