Suppose we have a sentence S in first order logic and it's corrospoding sentence S' in second order logic (by simply replacing any predicates in S with variables).
What can be said about S' if?
a) If S is satisfiable?
b) S is valid?
c) S is true in a model of size k?
d) S is true in an infinite model?
I can't find any information about this online, and was wondering if someone could guide me in the right direction.
Thanks