The scope of Feferman’s semi-intuitionistic set theories and his second conjecture

The paper is concerned with the scope of semi-intuitionistic set theories that relate to various foundational stances. It also provides a proof for a second conjecture of Feferman’s that relates the concepts for which the law of excluded middle obtains to those that are absolute with regard to the relevant test structures, or more precisely of ∆1 complexity. The latter is then used to show that a plethora of statements is indeterminate with respect to various semi-intuitionistic set theories.