More on the correspondence intuition

Introduce the notion "SatCorr", where SatCorr(p,T) iff p is a proposition, T is a partial theory of truth, and T satisfies the correspondence intuition in respect of p. I think the following are true:

1. If SatCorr(p,T) and SatCorr(q,T), then SatCorr(p or q,T), SatCorr(p and q,T) and SatCorr(not p,T).
2. If T says that singular existential propositions are made true by and only by the the objects they report the existence of, and p is any singular existential proposition, then SatCorr(p,T).

A consequence of (1) and (2) is that the correspondence intuition does not require truthmakers for all truths. For if we accept (1) and (2), any theory like T in (2) will automatically satisfy the correspondence intution for conjunctions, disjunctions and negations of singular existential propositions—even if it does not provide truthmakers for these.