Square below a non-weakly compact cardinal.

In his seminal paper introducing the fine structure of L, Jensen (Ann Math Log 4:229–308, 1972) proved that under V = L any regular cardinal that reflects stationary sets is weakly compact. In this paper we give a new proof of Jensen's result that is straight-forward and accessible to those without a knowledge of Jensen's fine structure theory. The proof here instead uses hyperfine structure, a very natural and simpler alternative to fine structure theory introduced by Friedman and Koepke (Bull Symb Log 3:453–468, 1997). [ABSTRACT FROM AUTHOR]