I could search the book for the notations Cn, Ae and ThN, but to speed things up, could you remind what they stand for?
Here is problem 10 from Section 3.5 of Enderton's "A Mathematical Introduction to Logic":
The theory Cn Ae has many complete extensions, of which ThN is but one. How many? That is, what is the cardinality of the set of complete theories (in the language) that extend Ae?
Does anyone know how to answer this question?