Vopěnka's Principle without Choice: Preservation under Symmetric Extensions

Tom de Groot, Wojciech Aleksander Wołoszyn

We give a detailed proof that every set-sized symmetric extension of a model of $\mathsf{ZF}+\mathsf{VP}$ again satisfies $\mathsf{ZF}+\mathsf{VP}$, where $\mathsf{VP}$ is formulat…