Short proof that Vopěnka's Principle is symmetrically stable

Abstract

We show that Vopěnka's Principle is stable under symmetric extensions. Recently, de Groot and Woloszyn [1] proved this fact. We found the proof of this theorem unnecessarily complicated. In this short note we prove the same statement. We direct the reader to [3] for an exposition on symmetric extensions.

arXiv comment2 pages; short proof for a theorem from arXiv paper 2609.06856