AAxiom cardinalF is calledthe Mahlostatement ifthat every normal function on itthe ordinals has a regular fixed point. (This is not a first-order axiom as it quantifies over all normal functions, so theit can be considered either as a second-order axiom or as an axiom (scheme.) A statingcardinal thatis called Mahlo if "every normal function on the ordinalsit has a regular fixed point", so axiom F is in some sense saying that the class of all ordinals is Mahlo. ThisA cardinal κ is Mahlo if and only if a second-order form of axiom F holds in ''V''<sub>κ</sub>. Axiom F is in turn equivalent to the statement that for any formula φ with parameters there are arbitrarily large inaccessible ordinals α such that ''V''<sub>α</sub> reflects φ (in other words φ holds in ''V''<sub>α</sub> if and only if it holds in the whole universe) {{harv|Drake|1974|loc=chapter 4}}.