Frege's Puzzle and Naive Theory

Nathan Salmon in Frege's Puzzle on the distinction between intension and extension:

"The intension of a singular term, sentence, or predicate is a function that assigns to any possible world w the extension the singular term, sentence, or predicates takes on with respect to w. The extension of a singular term (with respect to a possible world w) is simply its referent (with respect to w), i.e., the object or individual to which the term refers (with respect to w). The extension of a sentence (with resp3ect to w) is its truth value (with respect to w)--either truth or falsehood. The extension of an n-place predicate (with respect to w) is the predicate's semantic characteristic function (with respect to w), i.e., the function that assigns either truth or falsehood to an n-tuple of individuals, according as the predicate or its negation applies (with respect to w) to the n-tuple. Assuming bivalence, the extension of an n-place predicate may be identified instead with the class or n-tuples to which the predicate applies." p.14