In this talk, we will show the result of Morley that the number of countable models for a theory must be either at most $\aleph_1$ or $2^{\aleph_0}$. The proof splits into two cases showcasing different areas of logic: model theoretic arguments for the at most $\aleph_1$ case and descriptive set theory showing all others must have $2^{\aleph_0}$ models.
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