Let define cardinal $\kappa$ as hyper-Berkeley if for any transitive set $M$ such that $\kappa\in M$ there exist elementary embedding $j: M\prec M$ with fixed point $\lambda$ and $\text{crit}j\lt\lambda<\kappa$.

1. Are hyper Berkeley cardinals equiconsistent with $\sf ZF$+"club Berkeley cardinal"?
2. Are hyper Berkeley cardinals equiconsistent with $\sf ZF+BC$ (Berkeley cardinal)?

Let's define cardinal $\kappa$ as hyper-Berkeley if for any transitive set $M$ such that $\kappa\in M$ there exists an elementary embedding $j: M\prec M$ with fixed point $\lambda$ and $\text{crit}j\lt\lambda<\kappa$.

1. Are hyper Berkeley cardinals equiconsistent with $\sf ZF$+"club Berkeley cardinal"?
2. Are hyper Berkeley cardinals equiconsistent with $\sf ZF+BC$ (Berkeley cardinal)?

Let define cardinal $\kappa$ as hyper-Berkeley if for any transitive set $M$ what $\kappa$ $\in M$ exist elementary embedding $j$ where fixed point $\lambda$ above critical and $\lambda<\kappa$.

1. This cardinal is equiconsistent with $\sf ZF$+"club Berkeley cardinal"?
2. Are consistent to $\sf ZF+BC$ (Berkeley cardinal)?

Let define cardinal $\kappa$ as hyper-Berkeley if for any transitive set $M$ such that $\kappa\in M$ there exist elementary embedding $j: M\prec M$ with fixed point $\lambda$ and $\text{crit}j\lt\lambda<\kappa$.

1. Are hyper Berkeley cardinals equiconsistent with $\sf ZF$+"club Berkeley cardinal"?
2. Are hyper Berkeley cardinals equiconsistent with $\sf ZF+BC$ (Berkeley cardinal)?

Let define cardinal $\kappa$ as hyper-Berkeley if for any transitive set $M$ what $\kappa$ $\in M$ exist elementary embedding $j$ where fixed point $\lambda$ above critical and $\lambda<k$.

1. This cardinal is equiconsistent with $ZF$+"club Berkeley cardinal"?
2. Are consistent to $ZF+BC$ (Berkeley cardinal)?

Let define cardinal $\kappa$ as hyper-Berkeley if for any transitive set $M$ what $\kappa$ $\in M$ exist elementary embedding $j$ where fixed point $\lambda$ above critical and $\lambda<\kappa$.

1. This cardinal is equiconsistent with $\sf ZF$+"club Berkeley cardinal"?
2. Are consistent to $\sf ZF+BC$ (Berkeley cardinal)?