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A cardinal $\kappa$ is a Vopěnka cardinal just in case Vopěnka's principle holds in $V_\kappa$.

Suppose that $\kappa$ and $\lambda$ are both Vopěnka cardinals with $\lambda > \kappa$. Must it be the case that $V_\lambda \vDash$ '$\kappa$ is a Vopěnka cardinal'?

(Understand the predicate "… is a Vopěnka cardinal" after the turnstile as standing for a schema, since the informal claim is not directly expressible in $\mathsf{ZFC}$.)

A cardinal $\kappa$ is a Vopěnka cardinal if Vopěnka's principle holds in $V_\kappa$.

Suppose that $\kappa$ and $\lambda$ are both Vopěnka cardinals with $\lambda > \kappa$. Must it be the case that $V_\lambda \vDash$ '$\kappa$ is a Vopěnka cardinal'?

(Understand that the predicate "… is a Vopěnka cardinal" after the turnstile as standing for a schema, since the informal claim is not directly expressible in $\mathsf{ZFC}$.)

A cardinal $\kappa$ is a Vopěnka cardinal just in case Vopěnka's principle holds in $V_\kappa$.

Suppose that $\kappa$ and $\lambda$ are both Vopěnka cardinals with $\lambda > \kappa$. Must it be the case that $V_\lambda \vDash$ "$V_\kappa$ is a Vopěnka cardinal"?

(Understand the predicate "… is a Vopěnka cardinal" after the turnstile as standing for a schema, since the informal claim is not directly expressible in $\mathsf{ZFC}$.)

A cardinal $\kappa$ is a Vopěnka cardinal just in case Vopěnka's principle holds in $V_\kappa$.

Suppose that $\kappa$ and $\lambda$ are both Vopěnka cardinals with $\lambda > \kappa$. Must it be the case that $V_\lambda \vDash$ '$\kappa$ is a Vopěnka cardinal'?

(Understand the predicate "… is a Vopěnka cardinal" after the turnstile as standing for a schema, since the informal claim is not directly expressible in $\mathsf{ZFC}$.)

A cardinal $\kappa$ is a Vopěnka cardinal just in case Vopěnka's principle holds in $V_\kappa$.

Suppose that $\kappa$ and $\lambda$ are both Vopěnka cardinals with $\lambda > \kappa$. Must it be the case that $V_\lambda \vDash$ "$V_\kappa$ is a Vopěnka cardinal"?

A cardinal $\kappa$ is a Vopěnka cardinal just in case Vopěnka's principle holds in $V_\kappa$.

Suppose that $\kappa$ and $\lambda$ are both Vopěnka cardinals with $\lambda > \kappa$. Must it be the case that $V_\lambda \vDash$ "$V_\kappa$ is a Vopěnka cardinal"?

(Understand the predicate "… is a Vopěnka cardinal" after the turnstile as standing for a schema, since the informal claim is not directly expressible in $\mathsf{ZFC}$.)