Recursive Analogues of Shrewdness and Subtlety, with Applications to Fine Structure

We share both recent and older, well-known results regarding the notions of stable ordinals and shrewd cardinals. We then argue that ${\mathrm{\Sigma }}_2$-nonprojectible ordinals may be considered as recursive analogues to subtle cardinals, a highly combinatorial type of cardinal related to Jensen’s fine structure, due to the latter possessing a characterisation in terms of shrewdnesss.