Using Replacement Schema we can prove any wellordering is isomorphic to an ordinal number.
Q: Is the following consistent?
$ZFCRep+\neg Rep+\text{Any wellordering is isomorphic to an ordinal number}$
Using Replacement Schema we can prove any wellordering is isomorphic to an ordinal number. Q: Is the following consistent? $ZFCRep+\neg Rep+\text{Any wellordering is isomorphic to an ordinal number}$ 


Let $\kappa$ be a $\beth$fixed point  that is, let $\kappa = \beth_\kappa$. Then $V_\kappa$ models ZFC  Rep + "every wellorder is isomorphic to an ordinal". But ZFC proves the existence of $\beth$fixed points. Thus, when $\kappa$ is the least such fixed point, $V_\kappa$ models ZFC  Rep + "every wellorder is isomorphic to an ordinal" but fails to model ZFC (since being a $\beth$fixed point is absolute for $V_\kappa$). 

