I have wondered for a while what gave rise to the notation $0^\sharp$. According to wikipedia this is due to Solovay in 1967, but (perhaps unsurprisingly) there's no discussion of why that notation was chosen. In contrast, Silver mentions in a paper that he chose the symbol $\Sigma$ to represent the same thing. Nonetheless, I couldn't turn anything up with a bit of searching.

So, why did Solovay choose zero-sharp as the name for this object? (The zero part at least makes sense in the general sense of $a^\sharp$ where we consider $L[a]$ instead of $L$) Especially given that there are plenty of ways of indicating something "a little bit more/different" that are quite normal in mathematical notation.