STPL := soundness theorem for predicate logic

(see this)




When trying to figure out the strength of the STPL in reverse mathematics, I managed to convince myself of the following:


a) ACA0 has a (provably) $\Delta_1^1$ pair of formulas, which it proves enough about to consider them as defining in it the truth predicate for first-order structures.

b) ACA0 does not prove the STPL using the truth predicate as defined in (a).

c) [ACA0 + [$\Delta_1^1$ induction]] does prove the STPL as given in (b).



So, my questions are:

1. Are my understandings correct?
   
   
2. Does ACA0 + STPL prove $\Delta_1^1$ induction?
   
   
3. Is anything else known about the positions of STPL and $\Delta_1^1$ induction in the reverse mathematics hierarchy? (For example, where would they go on the list on page 4 here?)